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

Question

UpStudy AI · Accepted Answer

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

2. The composition $$ f \circ g $$ is defined as:
   $$
   (f \circ g)(x)=f(g(x)).
   $$

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

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

5. Add $$ 4 $$ to obtain the final expression:
   $$
   6x-9+4=6x-5.
   $$

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

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