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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] New post  Updated on: 31 Oct 2012, 04:04
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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
Show Spoiler
E


Thanks & Regards
Vinni
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Originally posted by vinnik on 31 Oct 2012, 00:57.
Last edited by Bunuel on 31 Oct 2012, 04:04, edited 1 time in total.
Renamed the topic.
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Re: function [#permalink] New post  31 Oct 2012, 01:22
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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
Show 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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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post  22 Nov 2012, 05:23
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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
Show 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: function [#permalink] New post  31 Oct 2012, 21:00
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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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Re: function [#permalink] New post  31 Oct 2012, 21:31
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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] New post  20 Nov 2012, 10:23
2
Kudos
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
Show 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] New post  21 Nov 2012, 21:32
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
Show 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] New post  22 Nov 2012, 06:01
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] New post  22 Nov 2012, 06:03
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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] New post  05 Dec 2012, 21:58
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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Re: function [#permalink] New post  09 Feb 2013, 04:08
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
Show 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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Re: function [#permalink] New post  09 Feb 2013, 04:19
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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
Show 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] New post  22 Feb 2013, 22:27
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] New post  24 Feb 2013, 21:20
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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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Re: function [#permalink] New post  16 Mar 2013, 21:16
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
Show 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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Re: function [#permalink] New post  17 Mar 2013, 01:57
Expert Reply
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
Show 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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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post  22 May 2013, 06:56
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] New post  22 May 2013, 07:08
fozzzy wrote:
one more question if we were given X is positive or negative then the answer would be E?


Not sure of what you mean, but the answer is C for every value of x (+ve, -ve or =0)
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post  22 May 2013, 08:41
As per Vips000 solution after you solve we get \(=|x|\)

now if we were given an additional constraint that X is positive then we can solve for the modulus right?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post  22 May 2013, 08:45
fozzzy wrote:
As per Vips000 solution after you solve we get \(=|x|\)

now if we were given an additional constraint that X is positive then we can solve for the modulus right?


If we know that x is positive then we can solve the modulus and obtain \(|x|=x\), yes you're right.

But be careful, in this case both c and e would be correct

C). \(|x|\) => \(x\)

E). \(x\)
They are the same.

Hope it's clear
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
22 May 2013, 08:45
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