dont know how to start this:
$\displaystyle f(x) = 5 + 5 x + 4 e^x $
find $\displaystyle f^{-1}(9) = $____
There is a theorem that says:
Let $\displaystyle f$ be a one-to-one continuous function on an open interval $\displaystyle I$. If $\displaystyle f$ is differentiable at $\displaystyle x_0 \in I$ and if $\displaystyle f'(x_0) \neq 0$, then $\displaystyle f^{-1}$ is differentiable at $\displaystyle y_0 = f(x_0)$ and
$\displaystyle \left( f^{-1} \right)^{ \prime} (y_0) = \frac {1}{f'(x_0)}$
Note here, that $\displaystyle f(0) = 9$
Let $\displaystyle x_0 = 0$ and $\displaystyle y_0 = f(0) = 9$
Then $\displaystyle \left( f^{-1} \right)^{ \prime} (9) = \frac {1}{f'(0)}$
Now continue