QuestionFind the slope of the tangent line to $f^{-1}$ at the point $(1,-1)$ for $f(x)=(x+2)^{2}$ where $x \geq-2$. The slope is $\square$.

Studdy Solution
Plug in the value for the derivative of $f$ at $(-1,1)$ to calculate the derivative of $f^{-1}$ at $(1,-1)$.
$$\left(f^{-1}\right)'(1) = \frac{1}{2}$$The slope of the line tangent to the graph of $f^{-1}$ at $(1,-1)$ is $\frac{1}{2}$.