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

Question

UpStudy AI · Accepted Answer

1. Write down the definition of the composition:
   $$
   (f \circ g)(x) = f(g(x))
   $$

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

3. Using the function $$ f(x) = 3x + 4 $$, replace $$ x $$ with $$ 2x-3 $$:
   $$
   f(2x-3) = 3(2x-3) + 4
   $$

4. Simplify the expression by distributing and combining like terms:
   $$
   3(2x-3) + 4 = 6x - 9 + 4 = 6x - 5
   $$

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

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