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

Thanks & Regards

Vinni

Last edited by

Bunuel on 31 Oct 2012, 03:04, edited 1 time in total.

Renamed the topic.

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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

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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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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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 ]
20 Nov 2012, 09:23
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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

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 ]
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

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 ]
22 Nov 2012, 04:23
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink ]
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 ]
22 Nov 2012, 05:03

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

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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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

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 ]
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 ]
24 Feb 2013, 07:23

|x| is the answer. |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 ]
24 Feb 2013, 20:20
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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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

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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Let f(a) = a - 5 g(b) = 5 - b. [#permalink ]
22 May 2013, 01:02

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

Please Explain

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Re: Let f(a) = a - 5 g(b) = 5 - b. [#permalink ]
22 May 2013, 01:20

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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

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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