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

Question

UpStudy AI · Accepted Answer

Given:
$$
f(x) = 3x + 4, \quad g(x) = 2x - 3
$$
We need to find $$ f \circ g(x) $$, which means $$ f(g(x)) $$.

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

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

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

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

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