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

Question

UpStudy AI · Accepted Answer

To find the composition $$ f \circ g(x) $$, we need to evaluate $$ f(g(x)) $$. Here's how you can do it step by step:

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

**Step 1:** Find $$ g(x) $$
$$
g(x) = 2x - 3
$$

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

**Step 3:** Simplify the expression
$$
f(g(x)) = 3(2x) - 3(3) + 4 = 6x - 9 + 4 = 6x - 5
$$

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

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