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

Question

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1. We have the functions $$ f(x) = 3x + 4 $$ and $$ g(x) = 2x - 3 $$.

2. The composite function $$ f \circ g(x) $$ is defined as:
   $$
   f \circ g(x) = f(g(x))
   $$

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

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

5. Distribute the $$ 3 $$:
   $$
   3(2x - 3) = 6x - 9
   $$

6. Add $$ 4 $$ to complete the composite function:
   $$
   6x - 9 + 4 = 6x - 5
   $$

7. Therefore, the composite function is:
   $$
   f \circ g(x) = 6x - 5
   $$
$$ f \circ g(x) = 6x - 5 $$

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