Please Check My Work:

**qbkr21** · September 14th 2007, 08:42 PM

Thanks!!

-qbkr21

**topsquark** · September 15th 2007, 10:40 AM

Originally Posted by qbkr21

Thanks!!

-qbkr21

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

-Dan

**Jhevon** · September 15th 2007, 04:33 PM

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

**topsquark** · September 15th 2007, 05:22 PM

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

**qbkr21** · September 15th 2007, 07:05 PM

Thanks Guys!!

-qbkr21

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