To solve $(f \circ h)(3)$, we first need to understand that $(f \circ h)(x)$ means $f(h(x))$, meaning we substitute $h(x)$ into $f(x)$.

Given:

• $f(x) = 3x - 1$
• $h(x) = -x - 5$

Step-by-step solution:

1. Find $h(3)$: $h(3) = -(3) - 5 = -3 - 5 = -8$

2. Substitute $h(3)$ into $f(x)$: $f(h(3)) = f(-8) = 3(-8) - 1 = -24 - 1 = -25$

Thus, $(f \circ h)(3) = -25$.

Let me know if you'd like further clarification, or if you have any questions.

Here are 5 related questions to explore:

1. What is $(h \circ f)(2)$ given the same functions?
2. How do you interpret composition of functions graphically?
3. What happens if $f(x)$ and $h(x)$ are inverse functions?
4. Can you compute $(f \circ f)(x)$ for this specific $f(x)$?
5. How would the composition change if $f(x)$ were a quadratic function?

Tip: Always compute the inner function first when dealing with function compositions.