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

Question

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Simplify the expression by following steps:
- step0: Multiply the terms:
  $$f\left(gx\right)$$
- step1: Multiply the terms:
  $$fgx$$
Substitute $$ x=2x-3 $$ into the expression $$ 3(2x - 3) + 4 $$.
Evaluate the expression by following steps:
- step0: Evaluate:
  $$3\left(2x-3\right)+4$$
- step1: Substitute:
  $$3\left(2\left(2x-3\right)-3\right)+4$$
- step2: Subtract the terms:
  $$3\left(4x-9\right)+4$$
- step3: Expand the expression:
  $$12x-27+4$$
- step4: Add the numbers:
  $$12x-23$$
To find $$ f \circ g(x) $$, we need to substitute $$ g(x) $$ into $$ f(x) $$.

1. **Identify the functions:**
   - $$ f(x) = 3x + 4 $$
   - $$ g(x) = 2x - 3 $$

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

3. **Calculate $$ f(2x - 3) $$:**
   $$
   f(2x - 3) = 3(2x - 3) + 4
   $$

4. **Expand the expression:**
   $$
   = 6x - 9 + 4
   $$
   $$
   = 6x - 5
   $$

Thus, the result of $$ f \circ g(x) $$ is:
$$
f \circ g(x) = 6x - 5
$$
$$ f \circ g(x) = 6x - 5 $$

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

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