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

Question

UpStudy AI · Accepted Answer

To find the composition $$ f \circ g(x) $$, which is $$ f(g(x)) $$, follow these steps:

1. **Given Functions:**
   $$
   f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
   $$

2. **Compose $$ f $$ with $$ g $$:**
   $$
   f \circ g(x) = f(g(x))
   $$

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

4. **Simplify the Expression:**
   $$
   3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
   $$

5. **Final Result:**
   $$
   f \circ g(x) = 6x - 5
   $$

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

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