For $$ f(x)=3 x-3 $$ and $$ g(x)=4 x^{2}-3 $$, find the following functions. a. $$ (f \circ g)(x) $$; b. $$ (g \circ f)(x) $$; c. $$ (f \circ g)(-2) $$; d. $$ (g \circ f)(-2) $$ a. $$ (f \circ g)(x)=\square $$ (Simplify your answer.)

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To find $$ (f \circ g)(x) $$, we need to compose the functions $$ f $$ and $$ g $$. This means we substitute $$ g(x) $$ into $$ f(x) $$.

Given:
- $$ f(x) = 3x - 3 $$
- $$ g(x) = 4x^2 - 3 $$

**Step-by-Step Calculation:**

1. **Compose the Functions:**
   $$
   (f \circ g)(x) = f(g(x)) = f(4x^2 - 3)
   $$

2. **Substitute $$ g(x) $$ into $$ f(x) $$:**
   $$
   f(4x^2 - 3) = 3(4x^2 - 3) - 3
   $$

3. **Simplify the Expression:**
   $$
   3(4x^2 - 3) - 3 = 12x^2 - 9 - 3 = 12x^2 - 12
   $$

So, the simplified form of $$ (f \circ g)(x) $$ is:

$$
(f \circ g)(x) = 12x^2 - 12
$$

**Answer:**  
a. $$ (f \circ g)(x) = 12x^{2} - 12 $$
$$ (f \circ g)(x) = 12x^{2} - 12 $$

For and , find the following functions.
a. ; b. ; c. ; d.
a. (Simplify your answer.)

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