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# What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

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What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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30 Oct 2012, 23:57
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Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Oct 2012, 03:04, edited 1 time in total.
Renamed the topic.
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31 Oct 2012, 00:22
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vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..
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31 Oct 2012, 20:00
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Vips0000 wrote:
From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Well, I haven't understood completely.
All i know from my knowledge that |a - b| = |b - a|
So, as you have explained above |x-5|- |x-5| = 0
Now we are left with |-x|
According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5.
This is the exact reason i selected E as the answer.

I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement "It can not be E because x <> |x| for any negative value of x."

Thanks & Regards
Vinni
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31 Oct 2012, 20:31
1
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vinnik wrote:
Vips0000 wrote:
From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Well, I haven't understood completely.
All i know from my knowledge that |a - b| = |b - a|
So, as you have explained above |x-5|- |x-5| = 0
Now we are left with |-x|
According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5.
This is the exact reason i selected E as the answer.

I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement "It can not be E because x <> |x| for any negative value of x."

Thanks & Regards
Vinni

Two points that you are confused with:
|-x| = |x|
This is exactly same thing as you have mentioned:
"All i know from my knowledge that |a - b| = |b - a|"

Now second point,
x <> |x| for any negative number x.

Well, take for example x =-5
in this case, x= -5 and |x|=5
Are these 5 and -5 equal? no.
That is x <> |x| for any negative number x.

What you are confusing this is with |x|=|-x|

Hope it is clear.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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20 Nov 2012, 09:23
2
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vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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21 Nov 2012, 20:32
greatps24 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|

I am confused as in the value of |-x| will always be x so why are we choosing |x| ?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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22 Nov 2012, 04:23
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Expert's post
2013gmat wrote:
greatps24 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

how i solved this ques:

|f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5.

Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|

I am confused as in the value of |-x| will always be x so why are we choosing |x| ?

|-x|=|x| for all x's. Now, if x<0, then |-x|=|x|=-x but if x>=0, then |-x|=|x|=x.

Hope it's clear.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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22 Nov 2012, 05:01
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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22 Nov 2012, 05:03
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Expert's post
greatps24 wrote:
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?

|-x| and |x| are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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05 Dec 2012, 20:58
Bunuel wrote:
greatps24 wrote:
Kudos Bunuel. Thanks for clarifying

One point: what if in answer choices we also have |-x| (and |x|)?

|-x| and |x| are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices?

Kudos Bunuel. Cheers
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09 Feb 2013, 03:08
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x|
Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5|
If we simplify this we get two options |x-10| and |x|.
Why this is not correct ??
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09 Feb 2013, 03:19
1
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Expert's post
mani6389 wrote:
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Got a doubt...

f(g(x)| = |f(5-x)| = |5-x-5| =|-x|
Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5|
If we simplify this we get two options |x-10| and |x|.
Why this is not correct ??

|f(g(x))| has only one modulus.

g(x)=5-x, thus |f(g(x))| = |f(5-x)|.

Next, since f(5-x) = 5-x-5=-x, then |f(5-x)| = |-x| = |x|.

Hope it's clear.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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22 Feb 2013, 21:27
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....

when we put in the values appropriately:

|x-5|-|5-x|+|5-x-5|
=|-x|

mod of -x=x

i understand the piece tht

when we have the value as -x and we take modulous then it gives the values
as positive values of x.

|-x| is not equal to x

but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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24 Feb 2013, 07:23

|x| not necessarily is equal to x , as it would depend upon the whether x is +ve or -ve.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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24 Feb 2013, 20:20
Expert's post
1
This post was
BOOKMARKED
mehasingh wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A. |x - 10|
B. 3x + 10
C. |x|
D. |x - 5|
E. x

hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....

when we put in the values appropriately:

|x-5|-|5-x|+|5-x-5|
=|-x|

mod of -x=x

i understand the piece tht

when we have the value as -x and we take modulous then it gives the values
as positive values of x.

|-x| is not equal to x

but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x.

You are assuming that x is positive.

|-x| = |x| in any case. x may be positive or negative. Take examples:
Say x = 5, |-5| = |5| = 5
Say x = -5, |-(-5)| = |-5| = 5
Hence (C) is correct.

But to remove the mod, you must know the sign of x.

By definition,
|x| = x when x is positive
|x| = -x when x is negative

|-x| = |x| = x only when x is positive
If x is negative, say x = -1,
|-x| = |-(-1)| = 1 which is not the same as x.

Hence $$|-x| \neq x$$ when x is negative.
Since we have no information on the sign of x, we cannot say that |-x| = x.
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16 Mar 2013, 20:16
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Can any1 explain why

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

|5-x| = |x-5| ???

Thank you
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17 Mar 2013, 00:57
kuttingchai wrote:
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

Can any1 explain why

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

|5-x| = |x-5| ???

Thank you

Yes, |5-x| = |x-5|, because both represent the distance between x and 5.
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22 May 2013, 01:37
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

How did you get that part I didn't understand that I understood the rest why is it 5-x-5?
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22 May 2013, 01:40
fozzzy wrote:
Vips0000 wrote:
vinnik wrote:
Let f(a) = a - 5
g(b) = 5 - b.

What is the value of |f(x)| - |g(x)| + |f(g(x)| ?

A). |x - 10|
B). 3x + 10
C). |x|
D). |x - 5|
E). x

What is wrong with
[Reveal] Spoiler:
E

Thanks & Regards
Vinni

From question:

$$|f(x)| = |x-5|$$
$$|g(x)| =|5-x|$$
$$|f(g(x)| = |f(5-x)| = |5-x-5| =|-x|$$

Now:
$$|f(x)| - |g(x)| + |f(g(x)|$$

$$= |x-5| -|5-x|+|-x|$$

$$=|x-5|- |x-5|+|x|$$

$$=|x|$$

Ans C.

It can not be E because x <> |x| for any negative value of x.

Hope it helps..

How did you get that part I didn't understand that I understood the rest why is it 5-x-5?

This post might help: what-is-the-value-of-f-x-g-x-f-g-x-141632.html#p1180176
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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22 May 2013, 05:56
one more question if we were given X is positive or negative then the answer would be E?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?   [#permalink] 22 May 2013, 05:56

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