Question

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

Answer 1

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 | x is a real number}

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

Range = {y | y > 0}

Therefore, the correct option is A.

Answer 2

Answer:

A {x| x is a real number}; {y| y > 0}

Step-by-step explanation:

Edge 2021