To find the inverse of each given function, we need to follow these general steps:

1. Replace $f(x)$, $s(x)$, $h(x)$, or $r(x)$ with $y$.
2. Swap $x$ and $y$ in the equation.
3. Solve for $y$ in terms of $x$.
4. Replace $y$ with $f^{-1}(x)$, $s^{-1}(x)$, $h^{-1}(x)$, or $r^{-1}(x)$ as required.

Let's go through each function individually.

1. $f(x) = 11x + 9$

To find $f^{-1}(x)$:

1. Write $y = 11x + 9$.
2. Swap $x$ and $y$: $x = 11y + 9$.
3. Solve for $y$: $x - 9 = 11y$ $y = \frac{x - 9}{11}$
4. Thus, $f^{-1}(x) = \frac{x - 9}{11}$.

2. $s(x) = -\frac{15}{x + 3}$

To find $s^{-1}(x)$:

1. Write $y = -\frac{15}{x + 3}$.
2. Swap $x$ and $y$: $x = -\frac{15}{y + 3}$.
3. Solve for $y$: $-x = \frac{15}{y + 3}$ $-x(y + 3) = 15$ $-xy - 3x = 15$ $-xy = 15 + 3x$ [