Assume that f is a one to one function: If $f(x) = x^5 + x^3 +x$ , find $f^{-1}(3)$ and $f(f^{-1}(2))$

Question

If $f(x) = x^5 + x^3 +x$ , find $f^{-1}(3)$ and $f(f^{-1}(2))$

How do I go about solving this?

For example, since I am giving f inverse should $I = x^5 +x^3 + x = 3$ ?

Answer 1

In this case, you don't have to do very much. You can see just by examining the coefficients that $f(1) = 1^5 + 1^3 + 1 = 3$, so $f^{-1}(3) = 1$.

Since we're assuming that $f$ is one-to-one, that means precisely that $f(f^{-1}(x)) = x$ for all $x$. So $f(f^{-1}(2)) = 2$.