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The image contains a mathematical problem involving functions. Here's the information from the image:

Given:
- \( f(x) = x - 4 \)
- \( g(x) = x^2 - 1 \)

The task is to find \( g(f(x)) \), which is the composition of the two functions.

### Solution:
1. First, we know that \( f(x) = x - 4 \).
2. To find \( g(f(x)) \), we substitute \( f(x) \) into \( g(x) \).
3. The function \( g(x) = x^2 - 1 \), so we replace \( x \) with \( f(x) \):
   \[
   g(f(x)) = (f(x))^2 - 1 = (x - 4)^2 - 1
   \]
4. Now expand \( (x - 4)^2 \):
   \[
   (x - 4)^2 = x^2 - 8x + 16
   \]
5. Substitute this back into the expression for \( g(f(x)) \):
   \[
   g(f(x)) = x^2 - 8x + 16 - 1 = x^2 - 8x + 15
   \]

Thus, the correct answer is \( g(f(x)) = x^2 - 8x + 15 \).

Would you like any further details or clarification?

### Related Questions:
1. What is the definition of function composition?
2. How do you expand binomials like \( (x - 4)^2 \)?
3. How does substitution work when composing functions?
4. What are some common mistakes when performing function composition?
5. Can function composition be reversed? If so, how?

### Tip:
When performing function composition, always ensure that the result from the inner function is substituted entirely into the outer function.

If f(x) = x - 4 and g(x) = x^2 - 1, what is g(f(x))?

Explore how to solve the function composition problem g(f(x)) when f(x) = x - 4 and g(x) = x^2 - 1. This includes steps for substituting f(x) into g(x) and expanding the quadratic expression. Suitable for students in Grades 9-12.

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