The problem asks to find $g(f(x))$ given the functions $f(x) = 3x^2 + 5$ and $g(x) = x - 1$. Also, the expression for $f(x-1)$ is evaluated.

1. Problem Description

The problem asks to find $g(f(x))$ given the functions $f(x) = 3x^2 + 5$ and $g(x) = x - 1$. Also, the expression for $f(x-1)$ is evaluated.

2. Solution Steps

First we find $f(x-1)$:

$f(x-1) = 3(x-1)^2 + 5$.

$f(x-1) = 3(x^2 - 2x + 1) + 5$.

$f(x-1) = 3x^2 - 6x + 3 + 5$.

$f(x-1) = 3x^2 - 6x + 8$.

Next, we find $g(f(x))$:

$g(f(x)) = g(3x^2 + 5)$.

Since $g(x) = x - 1$, we have

$g(3x^2 + 5) = (3x^2 + 5) - 1$.

$g(3x^2 + 5) = 3x^2 + 4$.

3. Final Answer

$f(x-1) = 3x^2 - 6x + 8$.

$g(f(x)) = 3x^2 + 4$.