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

Question

UpStudy AI · Accepted Answer

1. Write the composition $$ f \circ g(x) = f(g(x)) $$.

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

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

4. Distribute the $$ 3 $$:
   $$
   3 \cdot 2x - 3 \cdot 3 + 4 = 6x - 9 + 4
   $$

5. Combine like terms:
   $$
   6x - 9 + 4 = 6x - 5
   $$

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

Solución de inteligencia artificial de Upstudy