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

Question

UpStudy AI · Accepted Answer

**Step 1: Write Down the Functions**

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

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

The composition $$ f \circ g(x) $$ is defined as:
$$
f \circ g(x) = f(g(x)).
$$
Substitute $$ g(x) $$ into $$ f(x) $$:
$$
f(g(x)) = 3(2x - 3) + 4.
$$

**Step 3: Simplify the Expression**

Distribute $$ 3 $$ inside the parentheses:
$$
3(2x - 3) = 6x - 9.
$$
Then, add $$ 4 $$:
$$
6x - 9 + 4 = 6x - 5.
$$

**Final Answer**

$$
f \circ g(x) = 6x - 5.
$$
$$ f \circ g(x) = 6x - 5 $$

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