To evaluate the composite function $(f \circ g)(-1)$, we first need to understand what a composite function is. A composite function $(f \circ g)(x)$ means applying $g(x)$ first and then applying $f$ to the result of $g(x)$.

Given:

• $f(x) = 11x$
• $g(x) = x^2 - 5$

Step 1: Evaluate $g(-1)$

We first substitute $x = -1$ into $g(x)$: $g(-1) = (-1)^2 - 5 = 1 - 5 = -4$

Step 2: Evaluate $f(g(-1))$

Now that we know $g(-1) = -4$, we substitute this value into $f(x)$: $f(g(-1)) = f(-4) = 11(-4) = -44$

Thus, $(f \circ g)(-1) = -44$.

Would you like further details, or do you have any questions?

Here are 5 related questions to expand your understanding:

1. How do you evaluate $(f \circ h)(2)$ for the given functions?
2. What is the difference between $f(g(x))$ and $g(f(x))$?
3. Can you solve $(g \circ f)(0)$ using the given functions?
4. What would be the result of $(h \circ g)(1)$?
5. How does one graph composite functions like $f(g(x))$?

Tip: When evaluating composite functions, always start by finding the value of the innermost function first, then apply the outer function to that result.