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

Question

UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Add the terms:
  $$3\left(2x-3\right)+4$$
- step1: Expand the expression:
  $$6x-9+4$$
- step2: Add the numbers:
  $$6x-5$$
To find $$ f \circ g(x) $$, we need to substitute $$ g(x) $$ into $$ f(x) $$.

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

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

3. Now, expand the expression:
   $$
   = 3 \cdot 2x - 3 \cdot 3 + 4 = 6x - 9 + 4
   $$

4. Combine like terms:
   $$
   = 6x - 5
   $$

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

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

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Algebra Questions