We are given two functions, $f(x) = x + 3$ and $g(x) = x^2 - 1$. We need to find the composite function $g(f(x))$, which is denoted as $g \circ f$.

1. Problem Description

We are given two functions, $f(x) = x + 3$ and $g(x) = x^2 - 1$. We need to find the composite function $g(f(x))$, which is denoted as $g \circ f$.

2. Solution Steps

The composite function $g(f(x))$ means that we need to substitute the function $f(x)$ into the function $g(x)$ wherever $x$ appears.

So, we replace $x$ in $g(x)$ with $f(x)$:

$g(f(x)) = (f(x))^2 - 1$

Since $f(x) = x + 3$, we have:

$g(f(x)) = (x + 3)^2 - 1$

Now we expand the square:

$(x + 3)^2 = (x + 3)(x + 3) = x^2 + 3x + 3x + 9 = x^2 + 6x + 9$

So, $g(f(x)) = x^2 + 6x + 9 - 1$

Finally, we simplify the expression:

$g(f(x)) = x^2 + 6x + 8$

3. Final Answer

$g(f(x)) = x^2 + 6x + 8$