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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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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   20 Nov 2013, 08:51
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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
Show 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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WilDThiNg
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] 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
Show 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] New post   14 Nov 2016, 05:30
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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.gmatclub.com/forum/veritas-prep-resource-links-no-longer-available-399979.html#/2015/0 ... s-on-gmat/
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] 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] 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
Show 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] New post   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!
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   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.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   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
Show Spoiler
E


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
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What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   22 Oct 2019, 06:13
vinnik wrote:
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)
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   08 Jun 2022, 00:07
Can I assume the reason why |5 - x| = |x-5| is cause of this:

|5-x|= |-(x-5)| and since the negative is in the modulus, it won't have an effect and remove it? Same reasoning applies to |-x|=|x|?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink] New post   20 Mar 2024, 21:04
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
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