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

Question

UpStudy AI · Accepted Answer

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

2. The composite function $$ f \circ g(x) $$ is defined as $$ f(g(x)) $$.

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

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

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

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

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