AP Precalculus / Unit 2: Exponential and Logarithmic Functions
2.8 Inverse Functions
Notes
$f^{-1}$ undoes $f$: $f(f^{-1}(x))=x$. Its graph reflects $f$ over $y=x$.
- To find it, swap $x$ and $y$, then solve for $y$.
- A function needs to be one-to-one to have an inverse (restrict the domain if needed).
Practice
The inverse of $f(x)=3x-6$:
Swap and solve: $x=3y-6$.
If $f(2)=7$, then $f^{-1}(7)=$
Inverses swap inputs and outputs.
The graph of $f^{-1}$ is the reflection of $f$ over:
Swapping coordinates.
Ready for more? Take the Unit 2 test.