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

Question

UpStudy AI · Accepted Answer

1. We need to compute the composition $$ f \circ g(x) = f(g(x)) $$.

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

3. The definition of $$ f(x) $$ is $$ f(x) = 3x + 4 $$, so replacing $$ x $$ with $$ 2x - 3 $$ yields:
   $$
   f(2x-3) = 3(2x-3) + 4
   $$

4. Distribute the $$ 3 $$ inside the parentheses:
   $$
   3(2x-3) = 6x - 9
   $$

5. Add $$ 4 $$ to the result:
   $$
   6x - 9 + 4 = 6x - 5
   $$

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

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