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We are given two functions, \( f(x) = 2x + 1 \) and \( g(x) = 2x^2 - 1 \), and asked to find \( f(g(-2)) \).

Here’s how we can solve this step by step:

1. First, find \( g(-2) \):
   \[
   g(x) = 2x^2 - 1
   \]
   Substituting \( x = -2 \):
   \[
   g(-2) = 2(-2)^2 - 1 = 2(4) - 1 = 8 - 1 = 7
   \]

2. Now that we know \( g(-2) = 7 \), we substitute \( 7 \) into the function \( f(x) \):
   \[
   f(x) = 2x + 1
   \]
   So, \( f(7) = 2(7) + 1 = 14 + 1 = 15 \).

Thus, \( f(g(-2)) = 15 \).

Would you like more details or explanations?

Here are 5 follow-up questions you might explore:
1. What happens if \( g(x) \) is a more complex polynomial?
2. Can you find \( g(f(-2)) \)?
3. How would you approach solving this problem if the functions were given as trigonometric functions instead?
4. What would be the result if \( f(x) \) were a logarithmic function and \( g(x) \) stayed the same?
5. How does function composition affect the domain and range of a function?

**Tip**: When composing functions, always evaluate the innermost function first!

If f(x) = 2x + 1 and g(x) = 2x^2 - 1, find f(g(-2)).

Learn how to solve the function composition problem f(g(-2)) where f(x) = 2x + 1 and g(x) = 2x^2 - 1. This step-by-step solution covers core concepts of function composition with linear and quadratic functions. Suitable for students in Grades 9-11.

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