Exercise 10

Let $h(x) = x + \sin(x)$.

1. Sketch a graph of $y = h(x)$ and explain why $h$ must be invertible.

2. Explain why it does not appear to be algebraically possible to determine a formula for $h^{-1}$.

3. Observe that the point $(\frac{\pi}{2}, \frac{\pi}{2} + 1)$ lies on the graph of $y = h(x)$. Determine the value of $(h^{-1})'(\frac{\pi}{2} + 1)$.