Function Inverses

To find the value of an inverse function at a specific point, $f^{-1}(c)$, it's faster to solve the equation $f(y) = c$ for $y$, rather than finding the general inverse function first.

For $f(x) = \frac{3}{2}x - 2$, to find $f^{-1}(3)$, set $3 = \frac{3}{2}y - 2$. Solving for $y$ gives $5 = \frac{3}{2}y$, so $y = \frac{10}{3}$.

For the special case $f(x) = \frac{ax+b}{cx+d}$, the inverse is $f^{-1}(x) = \frac{-dx+b}{cx-a}$.