Question

Determine the domain and range of the function (equation is below)

A. all real numbers; y > 0
B. x; y
C. x; y
D. x ≥ 0; y

Answer 1

A. all real numbers; y

Explanation:

We have been given the function
`f(x)=2(\sqrt[3]{108})^(2x)` and we are required to find domain and range of this function. In order to find domain and range of this function, let us first rewrite this function as an exponential function and simplify it as much as possible.

`f(x)=2(108^{(1)/(3)} )^(2x)`

`f(x)=2(108^{(2)/(3)} )^(x)`

This is an exponential function of the form
`f(x)=a\cdot b^(x)`

We know that domain of an exponential function is all real numbers and range is all positive real numbers.

Therefore, correct choice would be option (A).