Question

how to get f^-1(3) if f(x) = x^7 + x +1
(The answer is 1, but I don't know how to get to there).

Answer 1

First suppose that: \(f^{-1}(3) = x\).
This means \(f(f^{-1}(3)) = f(x) \implies f(x) = 3\).

So what we have is: \[
f(x) = 3 \implies 3 = x^7 + x +1
\]

Answer 2

Subtracting \(3\) from both sides gives us \[
0 = x^7+x-2
\]So you have to find the roots now.

Answer 3

You can find it relatively easy using TI-Nspire CAS calc. I wouldn't recommend trying to find it algebraically though.

Answer 4

Thank you!