Question

Given f(x)= 5x^3-9, find the inverse of f, f^-1(x)=?

Answer 1

to get the inverse, we just interchange the variables x and y, and solve for y> Recall that we can also substitute f(x) as y:

y = 5x^3 - 9
then we interchange x and y:
x = 5y^3 - 9
and we solve for y:
x + 9 = 5y^3
(x + 9)/5 = y^3
y = [(x + 9)/5]^(1/3)

then finally we substitute y for f'(x):
f'(x) = [(x + 9)/5]^(1/3)

hope this helps~ :)