Question

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

Answer 1

The inverse is

f^-1(x) = (1/√2)x^¼

And it is a function

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.