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

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Re: function [#permalink]  22 May 2013, 01:40
Expert's post
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]  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, 06:08
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]  22 May 2013, 07:41
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]  22 May 2013, 07:45
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]  20 Nov 2013, 07:51
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|

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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]  19 Feb 2015, 03:53
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?   [#permalink] 19 Feb 2015, 03:53

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

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