Find the inverse of the function. f(x) = 4x3 - 7

Hope you can see my working out that I attached below

f⁻¹(x) =   OR  

So practically what you do is take the f(x), original equation, and interchange the x and y and then solve for the new y.  This is a known fact since the inverse and original function are related by the domain (x values) of the function being the range of its inverse (y values) and the range of the function (y values) being the domain of its inverse (x values).