The problem asks us to calculate two composite functions: $f(g(0))$ and $g(f(0))$, given $f(x) = 2x - 1$ and $g(x) = 7 - x^2$.

1. Problem Description

The problem asks us to calculate two composite functions: $f(g(0))$ and $g(f(0))$, given $f(x) = 2x - 1$ and $g(x) = 7 - x^2$.

2. Solution Steps

(a) To find $f(g(0))$, we first evaluate $g(0)$.

$g(0) = 7 - (0)^2 = 7 - 0 = 7$.

Then we substitute this value into $f(x)$.

$f(g(0)) = f(7) = 2(7) - 1 = 14 - 1 = 13$.

(b) To find $g(f(0))$, we first evaluate $f(0)$.

$f(0) = 2(0) - 1 = 0 - 1 = -1$.

Then we substitute this value into $g(x)$.

$g(f(0)) = g(-1) = 7 - (-1)^2 = 7 - 1 = 6$.

3. Final Answer

(a) $f(g(0)) = 13$

(b) $g(f(0)) = 6$