We are tasked with finding $(f \circ h)(-3)$, which represents the composition of functions $f(x)$ and $h(x)$ evaluated at $x = -3$.

Given:

• $f(x) = 4x - 1$
• $h(x) = -x + 5$

The composition of functions $(f \circ h)(x)$ means $f(h(x))$. So, we first evaluate $h(-3)$ and then substitute that result into $f(x)$.

Step 1: Find $h(-3)$

$h(x) = -x + 5$ $h(-3) = -(-3) + 5 = 3 + 5 = 8$

Step 2: Find $f(h(-3)) = f(8)$

$f(x) = 4x - 1$ $f(8) = 4(8) - 1 = 32 - 1 = 31$

Thus, $(f \circ h)(-3) = 31$.

Would you like further clarification or details?

Here are 5 related questions to consider:

1. What is the general process of function composition?
2. How do we reverse the roles and calculate $(h \circ f)(-3)$?
3. Can we perform composition with more than two functions?
4. What happens if $f(x)$ and $h(x)$ are inverse functions?
5. How do compositions affect domain and range?

Tip: Always calculate the inner function in compositions first, then substitute its result into the outer function.