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The problem in your homework asks you to find \( (g \circ f)(1) \), which is the composite function of \( g \) and \( f \) evaluated at \( x = 1 \). Given the functions:

\[
f(x) = x^2 - 2
\]
and
\[
g(x) = 2x + 15
\]

We need to evaluate \( (g \circ f)(1) \), which means we first find \( f(1) \), then substitute that result into \( g(x) \).

### Step-by-step solution:
1. **Evaluate \( f(1) \):**
   \[
   f(1) = (1)^2 - 2 = 1 - 2 = -1
   \]
   
2. **Substitute \( f(1) = -1 \) into \( g(x) \):**
   \[
   g(-1) = 2(-1) + 15 = -2 + 15 = 13
   \]

Therefore, \( (g \circ f)(1) = 13 \).

Would you like more details on any part of this solution?

### Related questions:
1. How do you evaluate composite functions in general?
2. What is the difference between \( (g \circ f)(x) \) and \( (f \circ g)(x) \)?
3. How can we check if two functions are inverses of each other?
4. What are the domains and ranges of the given functions?
5. How do transformations of functions affect their graphs?

**Tip:** Always remember that for composite functions, you evaluate the inner function first, then use that result to evaluate the outer function.

Given that f(x) = x^2 - 2 and g(x) = 2x + 15, find (g ∘ f)(1), if it exists.

Learn how to evaluate the composite function (g ∘ f)(1) using the functions f(x) = x^2 - 2 and g(x) = 2x + 15. This problem covers key algebraic concepts, such as composite functions and function evaluation. Suitable for students in Grades 10-12.

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