Need help finding the inverse function?

Question

Find the inverse of the function of:

 

 

f(x)= 2x³ - 6

 

 

And verify that they are inverses.

Answer 1

f(x) = 2x³ - 6

x = 2(f^-1(x))³ - 6

x + 6 = 2(f^-1(x ))³

(x + 6) / 2 = (f^-1 (x))³

3√[(x + 6) / 2] = f^-1(x)