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Given the function h(x) and g(x).




Find g(h(-2))
.

 

Show all work for credit.

The problem requires finding \( g(h(-2)) \) given two functions: \( h(x) = x^2 - 2 \) and \( g(x) = 3x \).

### Steps:

1. **Find \( h(-2) \)**:
   \[
   h(x) = x^2 - 2
   \]
   Substituting \( x = -2 \):
   \[
   h(-2) = (-2)^2 - 2 = 4 - 2 = 2
   \]

2. **Use the result from \( h(-2) \) in \( g(x) \)**:
   \[
   g(x) = 3x
   \]
   Now, substitute \( x = 2 \) into \( g(x) \):
   \[
   g(2) = 3(2) = 6
   \]

Thus, \( g(h(-2)) = 6 \).

Would you like more details or have any questions about this? Here are some related questions:

1. How would you solve \( g(h(3)) \)?
2. What is the inverse of \( g(x) = 3x \)?
3. How does the composition of functions work for \( g(h(x)) \) in general?
4. What would change if \( h(x) \) was defined as \( x^2 + 2 \)?
5. Can you graph both functions \( h(x) \) and \( g(x) \)?

**Tip**: Always solve the inner function first when dealing with function compositions like \( g(h(x)) \).

Given the function h(x) = x^2 - 2 and g(x) = 3x, find g(h(-2)). Show all work for credit.

Solve the function composition problem g(h(-2)) where h(x) = x^2 - 2 and g(x) = 3x. This step-by-step solution covers algebraic concepts and function substitution. Suitable for Grades 7-9.

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