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.