If f(x) = x
2
- 4 and g(x) = x + 2, then the composite function (g o f)(x) is equal to:

To find the composite function \( (g \circ f)(x) \), we apply the function \( f(x) \) first and then apply the function \( g(x) \) to the result of \( f(x) \).

Given:
- \( f(x) = x^2 - 4 \)
- \( g(x) = x + 2 \)

We need to find \( (g \circ f)(x) \), which is equivalent to \( g(f(x)) \).

### Step-by-step solution:
1. First, find \( f(x) \):
   \[
   f(x) = x^2 - 4
   \]
   
2. Now, apply \( g(x) \) to \( f(x) \), which means we substitute \( f(x) \) into \( g(x) \):
   \[
   g(f(x)) = g(x^2 - 4)
   \]
   Since \( g(x) = x + 2 \), we replace \( x \) with \( x^2 - 4 \):
   \[
   g(x^2 - 4) = (x^2 - 4) + 2
   \]
   
3. Simplify:
   \[
   g(f(x)) = x^2 - 4 + 2 = x^2 - 2
   \]

So, the composite function \( (g \circ f)(x) \) is:
\[
(g \circ f)(x) = x^2 - 2
\]

Would you like more details or have any further questions?

Here are 5 related questions to explore:
1. How do you find the composite function \( (f \circ g)(x) \)?
2. What is the domain of the composite function \( (g \circ f)(x) \)?
3. How would the composite function change if \( g(x) = 2x + 3 \)?
4. Can you graph the composite function \( (g \circ f)(x) = x^2 - 2 \)?
5. How would you reverse the process and find the individual functions from a given composite function?

**Tip:** When working with composite functions, always apply the inner function first before applying the outer function!

If f(x) = x^2 - 4 and g(x) = x + 2, then the composite function (g o f)(x) is equal to:

Learn how to find the composite function g(f(x)) where f(x) = x^2 - 4 and g(x) = x + 2. This problem covers key algebraic concepts such as function composition and is suitable for students in Grades 9-10.

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