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

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UpStudy AI · Accepted Answer

Simplify the expression by following steps:
- step0: Multiply the terms:
  $$f\left(gx\right)$$
- step1: Multiply the terms:
  $$fgx$$
Expand the expression $$ 3(2x - 3) + 4 $$
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. We have the functions:
   $$
   f(x) = 3x + 4
   $$
   $$
   g(x) = 2x - 3
   $$

2. Now, we substitute $$ g(x) $$ into $$ f(x) $$:
   $$
   f(g(x)) = f(2x - 3)
   $$

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

4. Now, we expand this expression:
   $$
   = 6x - 9 + 4
   $$
   $$
   = 6x - 5
   $$

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

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