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

Question

UpStudy AI · Accepted Answer

To find $$ f \circ g(x) $$, we need to substitute $$ g(x) $$ into $$ f(x) $$.

1. First, we identify 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. Next, we replace $$ x $$ in $$ f(x) $$ with $$ 2x - 3 $$:
   $$
   f(2x - 3) = 3(2x - 3) + 4
   $$

4. Now, we will simplify the expression:
   $$
   f(2x - 3) = 6x - 9 + 4
   $$

5. Finally, we combine like terms:
   $$
   f(2x - 3) = 6x - 5
   $$

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

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