Question

Given that g(x) = x^5 - 5x^4 + 10x^3 - 10x^2 + 5x - 1, find g^-1(x).

Answer 1

First Factor.

$(x-1)^5 = x^5 -5x^4+10x^3 -10x^2+5x-1$

$g(x) = y = (x-1)^5$

Find inverse by solving for 'x'

$x-1 = y^{1/5} \\ \\ x = y^{1/5} +1 \\ \\ g^{-1} (x) = x^{1/5} + 1$