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

Question

UpStudy AI · Accepted Answer

**Step 1: Understand the composition**

We need to compute the composition $$ f \circ g(x) $$, which is defined as:
$$
f \circ g(x) = f(g(x))
$$

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

Given:
$$
g(x) = 2x - 3
$$
and
$$
f(x) = 3x + 4
$$
Substitute $$ g(x) $$ into $$ f $$:
$$
f(g(x)) = f(2x-3)
$$

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

Replace $$ x $$ in $$ f(x) $$ with $$ 2x-3 $$:
$$
f(2x-3) = 3(2x-3) + 4
$$

**Step 4: Simplify the expression**

Distribute $$ 3 $$ and simplify:
$$
3(2x-3) + 4 = 6x - 9 + 4 = 6x - 5
$$

**Final Answer**

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

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