Math Help - Solving for x given f^-1(x) and secondary equation

1. Solving for x given f^-1(x) and secondary equation

Hello,
I am starting out in Calc and this popped up on the first hw/pretest:

Solve 2 f(x-1)-2=0 for x if f^-1(x)=x^5+x

I figured f(x-1)=1 and "x=y(y^4+1)" is as far as I got with flipping the inverse.. My algebra is rusty and I'm stuck.

2. Re: Solving for x given f^-1(x) and secondary equation

Originally Posted by MickSinclair
Hello,
I am starting out in Calc and this popped up on the first hw/pretest:

Solve 2 f(x-1)-2=0 for x if f^-1(x)=x^5+x

I figured f(x-1)=1 and "x=y(y^4+1)" is as far as I got with flipping the inverse.. My algebra is rusty and I'm stuck.
$2 f(x-1) - 2 = 0$

$f(x-1) = 1 \implies f^{-1}(1) = x-1$

$x = f^{-1}(1) + 1 = 1^5 + 1 + 1 = 3$