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

Question

UpStudy AI · Accepted Answer

**Step 1: Write down the composite function**

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

The composite function $$ f \circ g(x) $$ is defined as:
$$
f \circ g(x) = f(g(x))
$$

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

Substitute $$ g(x) = 2x - 3 $$ into $$ f(x) $$:
$$
f(g(x)) = f(2x - 3)
$$

**Step 3: Evaluate $$ f(2x - 3) $$**

Using the definition of $$ f(x) $$, we replace $$ x $$ with $$ 2x - 3 $$:
$$
f(2x - 3) = 3(2x - 3) + 4
$$

**Step 4: Simplify the expression**

First, distribute the $$ 3 $$:
$$
3(2x - 3) = 6x - 9
$$
Then, add $$ 4 $$:
$$
6x - 9 + 4 = 6x - 5
$$

**Final Answer:**

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

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