determine the inverse, f^-1, of f when f(x)= 5-2x^3

y = 5 - 2 x^3

2x^3 = 5-y
x = [(5-y)/2]^1/3

f^-1(x) = [(5-x)/2]^1/3 is the inverse function. Plugging in f(x) gives you back x.