Given f (x) = 4x^4 find f^-1 (x) Then state whether f^-1 (x) is a function

The inverse is

f^-1 (x) = (1/√2) x^¼

And it is a function

Step-by-step explanation:

Given f (x) = 4x^4

Let y = f (x), so that

y = 4x^4

Then dividing both sides by 4

x^4 = y/4

Taking the fourth root of both sides

x = (y/4) ^¼

x = (1/√2) y^¼ = f^-1 (y)

Put y = x

y = (1/√2) x^¼ = f^-1 (x)

This is the inverse.

f^-1 (x) is a function.