# Math Help - Please Check My Work:

1. ## Please Check My Work:

Thanks!!

-qbkr21

2. Originally Posted by qbkr21
Thanks!!

-qbkr21
Maybe I'm being a little dense. How did you know that $f^{-1}(2) = 1$?

-Dan

3. Originally Posted by topsquark
Maybe I'm being a little dense. How did you know that $f^{-1}(2) = 1$?

-Dan
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 $f^{-1}(2) = 1$ just by looking at $f(x)$ and mentally plugging in values and working backwards. however, if that does not suffice you, note that $f^{-1}(2)$ is the solution to the following equation:

$f(x) = x^5 - x^3 + 2x = 2$

$\Rightarrow x^5 - x^3 + 2x - 2 = 0$

$\Rightarrow (x - 1) \left( x^4 + x^3 + 2 \right) = 0$

$\Rightarrow x = 1 \mbox { or } x^4 + x^3 + 2 = 0$

the last equation has no real solutions, so we take $x = 1$

thus, $f^{-1}(2) = 1$

EDIT: Oh, and, yes, it looks good, qbkr21

4. Originally Posted by Jhevon
it is almost obvious to see that $f^{-1}(2) = 1$ just by looking at $f(x)$ and mentally plugging in values and working backwards.
Doh! (We really need a Homer smiley.)

-Dan

5. ## Re:

Thanks Guys!!

-qbkr21