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

Question

UpStudy AI · Accepted Answer

We begin by finding $$ f(g(x)) $$.

1. Substitute $$ g(x) $$ into $$ f(x) $$:
   $$
   f(g(x)) = f(2x-3) = 3(2x-3) + 4
   $$

2. Distribute and simplify:
   $$
   3(2x-3) = 6x - 9
   $$
   So we have:
   $$
   f(g(x)) = 6x - 9 + 4
   $$

3. Combine like terms:
   $$
   f(g(x)) = 6x - 5
   $$

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

Solución de inteligencia artificial de Upstudy