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

Question

UpStudy AI · Accepted Answer

1. First, recall the definition of the composition of functions: $$ f \circ g(x) = f(g(x)) $$.

2. Given $$ g(x) = 2x-3 $$, substitute $$ g(x) $$ into $$ f(x) $$:
   $$
   f(g(x)) = f(2x-3)
   $$

3. The function $$ f(x) $$ is given by $$ f(x) = 3x + 4 $$. Replace $$ x $$ with $$ 2x-3 $$:
   $$
   f(2x-3) = 3(2x-3) + 4
   $$

4. Distribute the $$ 3 $$ and simplify:
   $$
   3(2x-3) + 4 = 6x - 9 + 4 = 6x - 5
   $$

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

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