Question

For which functions does f(-1/2)=/ - 1?A. f(x) = 2xB. f(x) =[x]c. f(x) = |--2x]D. f(x) = [2x]

Answer 1

We need to substitute the value of

`x=(-1)/(2)`

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:

`f((-1)/(2))=2((-1)/(2))=-1`

Opcion B. f(x) = ||x|| ---> where ||x|| means the nearest integer to x.

Substituting x = -1/2 we get:

`f((-1)/(2))=\left\Vert (-1)/(2)\left\Vert =-1\right?\right?`

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:

`f((-1)/(2))=|-2((-1)/(2))|=|1|=1`

Which is different from -1. So the answer is C. f(x) = |-2x|