ConkergMat wrote:

Function F(x) is defined as follows:

if x is positive or 0 then F(x) = 1 - x;

if x is negative then F(x) = x - 1.

Which of the following is true about F(x)?

I. \(F(|x|) = |F(x)|\)

II. \(F(x) = F(-x)\)

III. \(|F(x + 1)| = |x|\)

I. \(F(|x|) = |F(x)|\) :- not possible.

First, \(F(|x|)\) could be -ve, 0 and +ve but \(|F(x)|\) is always 0 or +ve.

If |x| is greater than 1, \(F(|x|)\) = 1 - lxl is -ve fraction or > 1.

If |x| is smaller than 1, \(F(|x|)\) = 1 - |x| is +ve fraction.

If |x| is 0, \(F(|x|)\) is 1.

But \(|F(x)|\) is always 0 or +ve. So not true.

II. \(F(x) = F(-x)\):- not possible.

If x is +ve, -x is -ve and vice versa.

If x is 0, F(x) = F(-x) = 1

If x is +ve, F(x) = 1 - x, which could be +ve if x is smaller than 1 or -ve if x is > 1, and F(-x) = -x-1, which could also be -ve if x is >-1 or +ve if x is <-1.

Similarly, if x is negative, then F(x) and F(-x) will have +ve or -ve values.

They are not equal. not suff.

III. \(|F(x + 1)| = |x|\):- is possible.

\(|F(x + 1)|\) is always \(|x|\) whether (x+1) is +ve or -ve.

If \((x + 1)\) is +ve, \(|F(x + 1)|\) = \(|1- (x + 1)|\) = \(|x|\)

If \((x + 1)\) is -ve, \(|F(x + 1)|\) = \(|(x + 1)-1|\) = \(|x|\)

III is true.

_________________

Verbal: new-to-the-verbal-forum-please-read-this-first-77546.html

Math: new-to-the-math-forum-please-read-this-first-77764.html

Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html

GT