To find $(f \circ h)(-7)$, we need to evaluate $f(h(-7))$.

1. Find $h(-7)$: $h(x) = -x + 5$ Substitute $x = -7$: $h(-7) = -(-7) + 5 = 7 + 5 = 12$

2. Now find $f(h(-7)) = f(12)$: $f(x) = -2x - 1$ Substitute $x = 12$: $f(12) = -2(12) - 1 = -24 - 1 = -25$

So, $(f \circ h)(-7) = -25$.

Final Answer:

$(f \circ h)(-7) = -25$

Would you like further clarification or details on any of the steps?

Here are related questions to practice:

1. Find $(h \circ f)(-7)$ given $f(x) = -2x - 1$ and $h(x) = -x + 5$.
2. Determine $(f \circ h)(3)$ for the same functions $f(x)$ and $h(x)$.
3. If $g(x) = 3x - 4$, compute $(f \circ g)(2)$ with $f(x)$ as defined above.
4. Solve for $(f \circ f)(x)$ when $f(x) = -2x - 1$.
5. Find the domain of $f(h(x))$ when $f(x) = -2x - 1$ and $h(x) = -x + 5$.

Tip: For composite functions, always work from the inside out!