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

Question

UpStudy AI · Accepted Answer

To find the composition $$ f \circ g(x) $$, we need to evaluate $$ f $$ at $$ g(x) $$. Here's a step-by-step breakdown:

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

**Step 1:** Write the composition $$ f \circ g(x) $$ as $$ f(g(x)) $$.

$$
f \circ g(x) = f(g(x))
$$

**Step 2:** Substitute $$ g(x) $$ into $$ f(x) $$.

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

**Step 3:** Replace $$ x $$ in $$ f(x) $$ with $$ 2x - 3 $$.

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

**Step 4:** Distribute and simplify.

$$
3(2x - 3) + 4 = 6x - 9 + 4 = 6x - 5
$$

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

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