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What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
 31 Oct 2012, 00:57
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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
Last edited by Bunuel on 31 Oct 2012, 04:04, edited 1 time in total.
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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 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.. 
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Vips0000 wrote: 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.. Well, I haven't understood completely. All i know from my knowledge that |a - b| = |b - a| So, as you have explained above |x-5|- |x-5| = 0 Now we are left with |-x| According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5. This is the exact reason i selected E as the answer. I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement " It can not be E because x <> |x| for any negative value of x." Thanks & Regards Vinni
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vinnik wrote: Vips0000 wrote: 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.. Well, I haven't understood completely. All i know from my knowledge that |a - b| = |b - a| So, as you have explained above |x-5|- |x-5| = 0 Now we are left with |-x| According to what i have read from the books, any absolute value whether negative or positive will come out as positive. For eg. |-5| = 5. This is the exact reason i selected E as the answer. I must be missing one of the concepts. Can you please elaborate more on it. I didn't completely understand this statement " It can not be E because x <> |x| for any negative value of x." Thanks & Regards Vinni Two points that you are confused with: |-x| = |x| This is exactly same thing as you have mentioned: "All i know from my knowledge that |a - b| = |b - a|" Now second point, x <> |x| for any negative number x. Well, take for example x =-5 in this case, x= -5 and |x|=5 Are these 5 and -5 equal? no. That is x <> |x| for any negative number x. What you are confusing this is with |x|=|-x| Hope it is clear.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
20 Nov 2012, 10:23
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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 Thanks & Regards Vinni how i solved this ques: |f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5. Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x|
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
21 Nov 2012, 21:32
greatps24 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 how i solved this ques: |f(x)| - |g(x)| = 0. Because, f(x) and g(x) both represents distance between x & 5. Therefore, we have to solve only this |f(g(x)| => |f(5-x)|= |5-x-5| = |x| I am confused as in the value of |-x| will always be x so why are we choosing |x| ?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
22 Nov 2012, 05:23
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
22 Nov 2012, 06:01
Kudos Bunuel. Thanks for clarifying One point: what if in answer choices we also have |-x| (and |x|)?
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
22 Nov 2012, 06:03
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
05 Dec 2012, 21:58
Bunuel wrote: greatps24 wrote: Kudos Bunuel. Thanks for clarifying
One point: what if in answer choices we also have |-x| (and |x|)? |-x| and |x| are equal, thus we cannot have both of them among answer choices. Consider this, can we have both 4 and 2^2 among answer choices? Kudos Bunuel. Cheers
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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.. Got a doubt... f(g(x)| = |f(5-x)| = |5-x-5| =|-x| Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5| If we simplify this we get two options |x-10| and |x|. Why this is not correct ??
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mani6389 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.. Got a doubt... f(g(x)| = |f(5-x)| = |5-x-5| =|-x| Why (5-x) is considered without Mod sign. Ideally it should have been |f(|5-x|)| = |(|5-x|)-5| If we simplify this we get two options |x-10| and |x|. Why this is not correct ?? |f(g(x))| has only one modulus. g(x)=5-x, thus |f(g(x))| = |f(5-x)|. Next, since f(5-x) = 5-x-5=-x, then |f(5-x)| = |-x| = |x|. Hope it's clear.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
22 Feb 2013, 22:27
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
hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....
when we put in the values appropriately:
|x-5|-|5-x|+|5-x-5|
=|-x|
mod of -x=x
i understand the piece tht
when we have the value as -x and we take modulous then it gives the values
as positive values of x.
|-x| is not equal to x
but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
24 Feb 2013, 08:23
|x| is the answer.
|x| not necessarily is equal to x , as it would depend upon the whether x is +ve or -ve.
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Re: What is the value of |f(x)| - |g(x)| + |f(g(x)| ? [#permalink]
24 Feb 2013, 21:20
mehasingh 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
hi in the above question it is asking the value of the equation
|f(x)| - |g(x)| + |f(g(x)|....
when we put in the values appropriately:
|x-5|-|5-x|+|5-x-5|
=|-x|
mod of -x=x
i understand the piece tht
when we have the value as -x and we take modulous then it gives the values
as positive values of x.
|-x| is not equal to x
but here it is asking us the eventual result of the equation
so when we get |-x| we get the final result, it is positive values of x. You are assuming that x is positive. |-x| = |x| in any case. x may be positive or negative. Take examples: Say x = 5, |-5| = |5| = 5 Say x = -5, |-(-5)| = |-5| = 5 Hence (C) is correct. But to remove the mod, you must know the sign of x. By definition, |x| = x when x is positive |x| = -x when x is negative |-x| = |x| = x only when x is positive If x is negative, say x = -1, |-x| = |-(-1)| = 1 which is not the same as x. Hence |-x| \neq x when x is negative. Since we have no information on the sign of x, we cannot say that |-x| = x.
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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.. Can any1 explain why = |x-5| -|5-x|+|-x|=|x-5|- |x-5|+|x||5-x| = |x-5| ??? Thank you
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Let f(a) = a - 5 g(b) = 5 - b. [#permalink]
22 May 2013, 02:02
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
Please Explain
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Re: Let f(a) = a - 5 g(b) = 5 - b. [#permalink]
22 May 2013, 02:20
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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?
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