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.
_________________
Karishma
Veritas Prep GMAT Instructor
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