Which of the following functions has a domain of `x le 3` ?

Options

A. `f(x)=(3-x)^((1)/(4))+(x)/(2)`
B. `f(x)=(x-3)^((1)/(2))+(x)/(2)`
C. `f(x)=(x-2)^((1)/(3))+(x)/(4)`
D. `f(x)=(2-x)^((1)/(4))+(x)/(3)`

Answer

A

Explanation

The domian of a function cannot include numbers that figure into negative square roots. This means that any expression raised to a power of `(1)/(2)` or `(1)/(4)` must be greater than 0. x must be less than or equal to 3 when (3 - x) is raised to the `(1)/(4)` power. Any number greater than 3 would mean that a negative number is being raised to that power. So `f(x) = (3-x)^((1)/(4))+(x)/(2)` has a domain of `x le 3`.