The problem defines two functions $f(x) = 3x^2 - 1$ and $g(x) = 3 - x^2$. We need to find the value of $(g \circ f)(1)$ and choose the correct option among the given choices.

1. Problem Description

The problem defines two functions $f(x) = 3x^2 - 1$ and $g(x) = 3 - x^2$. We need to find the value of $(g \circ f)(1)$ and choose the correct option among the given choices.

2. Solution Steps

First, we need to find the value of $f(1)$.

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

$f(1) = 3(1)^2 - 1 = 3(1) - 1 = 3 - 1 = 2$

Next, we need to find the value of $g(f(1))$, which is $g(2)$.

$g(x) = 3 - x^2$

$g(2) = 3 - (2)^2 = 3 - 4 = -1$

Therefore, $(g \circ f)(1) = g(f(1)) = g(2) = -1$.

3. Final Answer

B. $(g \circ f)(1) = -1$