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

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SVP
Joined: 06 Sep 2013
Posts: 1660
Concentration: Finance
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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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

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
Manager
Joined: 29 Dec 2014
Posts: 66
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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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

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9224
Location: Pune, India
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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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/
_________________
Karishma
Veritas Prep GMAT Instructor

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Joined: 29 Dec 2014
Posts: 66
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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

Thanks
Manager
Joined: 23 Oct 2017
Posts: 63
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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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

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|
Intern
Joined: 02 Dec 2017
Posts: 2
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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04 Feb 2019, 15:02
Since, |f(x)| - |g(x)| cancel out each other, we are only left with |f(g(x)|. That brings us to option C!
Manager
Status: Gathering chakra
Joined: 05 Feb 2018
Posts: 249
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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10 Apr 2019, 11:33
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.
Intern
Joined: 23 Jul 2015
Posts: 31
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?  [#permalink]

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12 May 2019, 21:33
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

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|

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
Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ?   [#permalink] 12 May 2019, 21:33

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