We need to substitute the value of
[tex]x=\frac{-1}{2}[/tex]into the function of the options, and see which one is NOT equal to -1 (the symbol
≠
means "not equal to")
Option A. f(x) = 2x.
Substituting x = -1/2 we get:
[tex]f(\frac{-1}{2})=2(\frac{-1}{2})=-1[/tex]Opcion B. f(x) = ||x|| ---> where ||x|| means the nearest integer to x.
Substituting x = -1/2 we get:
[tex]f(\frac{-1}{2})=\left\Vert \frac{-1}{2}\left\Vert =-1\right?\right?[/tex]This because the nearest integer to -1/2 is -1
Option C. f(x) = |-2x| where the bars mean absolute value, which is that we will always have something positive when there are absolute value bars.
Substituting x = -1/2 we get:
[tex]f(\frac{-1}{2})=|-2(\frac{-1}{2})|=|1|=1[/tex]Which is different from -1. So the answer is C. f(x) = |-2x|
