let f(x) =11x, g(x) = $$ x^2 $$-5, and h(x) =2 (x-4). Evaluate each composite functions of                                                                      (f.g )(-1)

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.

Let f(x) = 11x, g(x) = x^2 - 5, and h(x) = 2(x - 4). Evaluate each composite function of (f ∘ g)(-1).

Learn how to evaluate the composite function (f ∘ g)(-1) for f(x) = 11x and g(x) = x^2 - 5. This step-by-step solution guides you through function composition and evaluation, covering key algebra concepts. Ideal for high school students in Grades 9-12.

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