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

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

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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|

Kudos Rain!!
Cheers
J

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

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12 Nov 2016, 09:44
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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14 Nov 2016, 04:30
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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14 Nov 2016, 07:27
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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07 Jan 2018, 07:11
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|

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

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