$$ f(x) = 3x + 4 \quad g(x) = 2x - 3 $$ $$ \text{Find: } f \circ g(x) $$

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

Given:
$$
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
$$

**Step 1:** Write the composition $$ f \circ g(x) $$ as $$ f(g(x)) $$.
$$
f \circ g(x) = f(g(x))
$$

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

**Step 3:** Replace every instance of $$ x $$ in $$ f(x) $$ with $$ 2x - 3 $$.
$$
f(2x - 3) = 3(2x - 3) + 4
$$

**Step 4:** Simplify the expression.
$$
= 3 \cdot 2x - 3 \cdot 3 + 4
$$
$$
= 6x - 9 + 4
$$
$$
= 6x - 5
$$

**Final Answer:**
$$
f \circ g(x) = 6x - 5
$$
$$ f \circ g(x) = 6x - 5 $$

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