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

Question

UpStudy AI · Accepted Answer

We are given:
$$
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3.
$$

To find $$ f \circ g(x) $$, we substitute $$ g(x) $$ into $$ f(x) $$:

1. Write $$ f(g(x)) $$:
   $$
   f(g(x)) = f(2x - 3).
   $$

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

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

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

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