How do you find the inverse of #f(x) = 1-x^3#?

Question

1166 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-08-05T18:07:58

Let #y = f(x) = 1 - x^3# and solve for #x# to derive:

#f^(-1)(y) = root(3)(1-y)#

Let #y = f(x) = 1 - x^3#

Add #x^3 - y# to both ends to get:

#x^3 = 1-y#

So:

#x = root(3)(x^3) = root(3)(1-y)#

So #f^(-1)(y) = root(3)(1-y)#