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

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To find the composition of the functions $$ f $$ and $$ g $$, denoted as $$ f \circ g(x) $$, follow these steps:

1. **Understand the Composition:**
   
   The composition $$ f \circ g(x) $$ means you first apply function $$ g $$ to $$ x $$, and then apply function $$ f $$ to the result of $$ g(x) $$. Mathematically, this is expressed as:
   $$
   f \circ g(x) = f(g(x))
   $$

2. **Substitute $$ g(x) $$ into $$ f(x) $$:**
   
   Given:
   $$
   g(x) = 2x - 3
   $$
   
   Substitute $$ g(x) $$ into $$ f(x) $$:
   $$
   f(g(x)) = f(2x - 3)
   $$
   
   Since $$ f(x) = 3x + 4 $$, replace $$ x $$ in $$ f $$ with $$ 2x - 3 $$:
   $$
   f(2x - 3) = 3(2x - 3) + 4
   $$

3. **Simplify the Expression:**
   
   Expand and simplify the expression:
   $$
   3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
   $$
   
4. **Final Result:**
   
   Therefore, the composition $$ f \circ g(x) $$ is:
   $$
   f \circ g(x) = 6x - 5
   $$

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

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