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

Question

UpStudy AI · Accepted Answer

```markdown
# Composition of Functions: $$ f \circ g(x) $$

Given the functions:
$$
f(x) = 3x + 4 \quad \text{and} \quad g(x) = 2x - 3
$$

To find the composition $$ f \circ g(x) $$, we compute $$ f(g(x)) $$:

$$
f(g(x)) = f(2x - 3) = 3(2x - 3) + 4
$$

Simplifying the expression:

$$
f(g(x)) = 6x - 9 + 4 = 6x - 5
$$

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

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