what is the inverse of h(x)=3x^3-45

y = 3x³ - 45

First step:  interchange x and y:

x  =  3y³ - 45

Second step:  solve for y:

Add 45 to both sides:                            x + 45  =  3y³

Divide both sides by 3:                    (x + 45)/3  =  y³

Find the cube root of both sides:     y  =  [ (x + 45)/3 ] ^ (1/3)

This last equation is the inverse function.