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

Question

UpStudy AI · Accepted Answer

1. We are given the functions
   $$
   f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3.
   $$

2. The composition $$ f \circ g(x) $$ means we apply $$ f $$ to the output of $$ g(x) $$:
   $$
   f \circ g(x) = f(g(x)).
   $$

3. Substituting $$ g(x) = 2x - 3 $$ into $$ f(x) $$, we get:
   $$
   f(g(x)) = 3(2x - 3) + 4.
   $$

4. Distributing and simplifying:
   $$
   3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5.
   $$

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

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