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

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Joined: 06 Sep 2013
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Concentration: Finance
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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New post 20 Nov 2013, 08:51
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


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|

Kudos Rain!!
Cheers
J :)
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Posts: 70
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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New post 12 Nov 2016, 10:44
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?


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

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New post 14 Nov 2016, 05:30
WilDThiNg wrote:
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.veritasprep.com/blog/2015/0 ... s-on-gmat/
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]

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New post 14 Nov 2016, 08:27
Yes, it does! Somehow, got lost somewhere.

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

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New post 07 Jan 2018, 08:11
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..:)

----------------
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|
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?   [#permalink] 07 Jan 2018, 08:11

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