For the pair of functions, find the indicated composition. a) Given functions $$ f(x)=4 x^{2}+3 x+5 $$ and $$ g(x)=3 x-3 $$. Find $$ (g \circ f)(x) $$.

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To find the composition of the functions $$ g $$ and $$ f $$, denoted as $$ (g \circ f)(x) $$, we need to substitute the function $$ f(x) $$ into the function $$ g(x) $$.

1. **Identify the functions:**
   - $$ f(x) = 4x^2 + 3x + 5 $$
   - $$ g(x) = 3x - 3 $$

2. **Substitute $$ f(x) $$ into $$ g(x) $$:**
   $$
   (g \circ f)(x) = g(f(x)) = g(4x^2 + 3x + 5)
   $$

3. **Replace $$ x $$ in $$ g(x) $$ with $$ f(x) $$:**
   $$
   g(4x^2 + 3x + 5) = 3(4x^2 + 3x + 5) - 3
   $$

4. **Distribute the 3:**
   $$
   = 12x^2 + 9x + 15 - 3
   $$

5. **Combine like terms:**
   $$
   = 12x^2 + 9x + 12
   $$

Thus, the composition $$ (g \circ f)(x) $$ is:
$$
(g \circ f)(x) = 12x^2 + 9x + 12
$$
$$ (g \circ f)(x) = 12x^2 + 9x + 12 $$

For the pair of functions, find the indicated composition. a) Given functions \( f(x)=4 x^{2}+3 x+5 \) and \( g(x)=3 x-3 \). Find \( (g \circ f)(x) \).

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