To determine

To find: Find the inverse function  f-1.

Answer

The inverse function is f-1x=log3⁡x+42

Explanation

Calculation:

Given:  y=32x-4

To find the inverse function f-1, we first write the function as . y=32x-4.

Since, ay=x⇔loga⁡x=y. Therefore, log3⁡y=2x-4

x=log3⁡y+42

We interchange x and y:

y=log3⁡x+42

Therefore, the inverse function is

f-1(x)=log3⁡x+42

Final statement:

The inverse function is f-1x=log3⁡x+42