Thanks!!
-qbkr21
For problems like these, you are usually given functions where you can tell what the inverse of a particular number is. it is almost obvious to see that $\displaystyle f^{-1}(2) = 1$ just by looking at $\displaystyle f(x)$ and mentally plugging in values and working backwards. however, if that does not suffice you, note that $\displaystyle f^{-1}(2)$ is the solution to the following equation:
$\displaystyle f(x) = x^5 - x^3 + 2x = 2$
$\displaystyle \Rightarrow x^5 - x^3 + 2x - 2 = 0$
$\displaystyle \Rightarrow (x - 1) \left( x^4 + x^3 + 2 \right) = 0$
$\displaystyle \Rightarrow x = 1 \mbox { or } x^4 + x^3 + 2 = 0$
the last equation has no real solutions, so we take $\displaystyle x = 1$
thus, $\displaystyle f^{-1}(2) = 1$
EDIT: Oh, and, yes, it looks good, qbkr21