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

Question

UpStudy AI · Accepted Answer

**Step 1:** Write down the given functions:

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

**Step 2:** Recall that the composition $$ f \circ g(x) $$ means substituting $$ g(x) $$ into $$ f(x) $$:

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

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

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

**Step 4:** Distribute the 3:

$$
3(2x - 3) = 6x - 9
$$

**Step 5:** Add 4 to the result:

$$
6x - 9 + 4 = 6x - 5
$$

**Final Answer:**

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

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