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

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jlgdr

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20 Nov 2013, 08:51

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vinnik

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

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Thanks & Regards
Vinni

Great problem!

Ya, just to keep it short and sweet

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

The first two terms are the same by property and the minus sign on the last term doesn't matter cause it will be positive under an absolute value.

So we are left with |x|

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WilDThiNg

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12 Nov 2016, 10:44

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fozzzy

Vips0000

vinnik

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

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?

Yes, please can u elaborate why |f(5−x)|=|5−x−5| and not I5 - (x-5)I - is there any fundamental concept i am missing.

Thanks

KarishmaB

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14 Nov 2016, 05:30

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WilDThiNg

Yes, please can u elaborate why |f(5−x)|=|5−x−5| and not I5 - (x-5)I - is there any fundamental concept i am missing.

Thanks

This is how functions work:
If we know that f(x) = x - 5,
f(a) = a - 5
f(2x) = 2x - 5
f(x+2) = (x + 2) - 5
f(g(x)) = g(x) - 5

Now, if we know that g(x) = 5 - x, then
f(g(x)) = 5 - x - 5

Does this help?

For more on functions, check: https://www.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... s-on-gmat/

luffy_ueki

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07 Jan 2018, 08:11

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Vips0000

vinnik

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

Thanks & Regards
Vinni

----------------
Since,

f(x)=x−5
|f(x)|=|x−5|

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

Now:
|f(x)|−|g(x)|+|f(g(x)|
Now observe magnitude wise- f(x) & g(x) will always be same and thus will cancel out each other thus the only remaining is |f(g(x))| = |-x|

rohitgupta2362

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04 Feb 2019, 15:02

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Since, |f(x)| - |g(x)| cancel out each other, we are only left with |f(g(x)|. That brings us to option C!

energetics

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10 Apr 2019, 11:33

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Nice question, I couldn't connect it to the rule that |a-b|=|b-a| so I just tested values:

if x input is 5, result is |5-5|-|5-5|+|5| = 0-0+5 = 5
so A, C and E are all possible.

if x input is -5, result is |-5-5|-|5-(-5)|+|-5| = 10-10+5 = 5, so only C works.

SPatel1992

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12 May 2019, 21:33

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vinnik

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

Thanks & Regards
Vinni

Hi! This is a really good question. Here's how I solved it:

Let x= 10

f(10) = 10-5 = 5
g(b) = 5-10 = -5

f(g(10) = f(-5) = -5-5= -10

Now, let's look at the equation:
|f(x)| - |g(x)| + |f(g(x)|
|5| - |-5| + |-10|
Ans: |-10|

Given answers:
A. |x - 10| = | 10-10| = |0| ~Wrong.
B. 3x + 10 = 30 + 10 = 40 ~ Wrong.
C. |x| = |10| ~ matches the derived ans
D. |x - 5| ~ |10-5| = |5| ~Wrong
E. x = 10 ~ Wrong

exc4libur

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22 Oct 2019, 06:13

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vinnik

Let f(a) = a - 5 and 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

$|f(x)| - |g(x)| + |f(g(x)|…|x-5|-|5-x|+|(5-x)-5|…|x-5|-|5-x|+|-x|$

$positive:[x-5≥0…x≥5];[5-x≥0…5≥x…x≤5];[-x≥0…x≤0]$

$negative:[x<5];[x>5];[x>0]$

$range:--0----5--$

$x>5:|x-5|-|5-x|+|-x|…(x-5)-(-(5-x))+(-(-x))…(x-5)-(-5+x)+x…x-5+5-x+x…=x$

$0<x≤5:|x-5|-|5-x|+|-x|…-(x-5)-(5-x)+(-(-x))…-x+5-5+x+x…-x+2x=x$

$x≤0:|x-5|-|5-x|+|-x|…-(x-5)-(5-x)+(-x)…-x+5-5+x-x…-2x+x=-x$

$|f(x)| - |g(x)| + |f(g(x)|=(x,-x)=|x|$

Answer (C)

MS26

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15 Aug 2025, 02:23

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f(x) = x - 5 and g(x) = 5 - x
f(g(x)) = g(x) - 5 = 5 - x - 5 = -x
|f(x)| - |g(x)| + |f(g(x)| = |x - 5| - | 5 - x| + |-x|
Since |x - 5| and | 5 - x| will give the same result , we can cancel them out.
So , |f(x)| - |g(x)| + |f(g(x)| = 0 + |-x| = |x|
C

vinnik

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

Thanks & Regards
Vinni