Question

What are the domain and range of the function f(x) = 4(RootIndex 3 StartRoot 81 EndRoot) Superscript x? x is a real number; y x > 4; y > 0 x; y > 4 x > 4; y

Answer 1

A x is a real number; y

Explanation:

Edge 2021

Answer 2

Given:

The function is

`f(x)=4(\sqrt[3]{81})^x`

To find:

The domain and range of the given function.

Solution:

Domain is the set of input values.

Range is the set of output values.

We have,

`f(x)=4(\sqrt[3]{81})^x`

It is an exponential growth function, where the initial value is 4 and the growth factor is
`(\sqrt[3]{81})`.

We know that the exponential function is defined for all real values of x. so,

Domain = x

In the given function 4>0 and
`(\sqrt[3]{81})^x>0` for all real values of x. So,

Range = y > 0

Therefore, the correct option is A.