$f^{–1}\left(\mathrm{(}x\mathrm{)}\right)$ = Inverse Function

Base Case: $f^{–1}\mathrm{(}x\mathrm{)}$

Note :

–          The notation on this can be a little hard to digest at first. What it says is given an inverse function, $f^{–1}\left(x\right)$, the derivative of that equation is found by following the derivative recipe. The recipe says put 1 over the derivative of your original $f\mathrm{(}x\mathrm{)}$,with the inverse plugged into it, $f\prime \mathrm{(}{f}^{–1}\left(x\right)\mathrm{)}$.

Important inverse ideas you should remember from algebra.

–           If you have a point, ( x , y ), on the original function, $f\mathrm{(}x\mathrm{)}$, then you are guaranteed to have the flipped point, ( y , x ), on the inverse function, $f^{–1}\left(x\right)$. If ( 5 , 3 ) is on the original function, then ( 3 , 5 ) is guaranteed to be on the inverse.

–           To find the inverse of an equation you will want to reverse the position of x and y , and then resolve to get y alone on one side of the equals. That result will be your inverse equation.

–           You use the Horizontal Line Test to determine if a function has an inverse.

You draw a horizontal line through the graph of your function.

• If it hits at two points, then you do not have an inverse.
• If it hits only at one point everywhere, then you do have an inverse.