To determine

To find: Find the inverse function  f-1.

Answer

The inverse function is g-1(x)=(4x-2)1/3

Explanation

Calculation:gx=log4⁡(x3+2)

 To find the inverse function g-1, we first write the function as y=log4⁡(x3+2).

Since,ay=x⇔loga⁡x=y. Therefore

4y=(x3+2)

x3=4y-2

x=(4y-2)1/3

We interchange  x and y:

y=(4x-2)1/3

Therefore, the inverse function is

f-1(x)=(4x-2)1/3

Final statement:

The inverse function is g-1(x)=(4x-2)1/3