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

Question

UpStudy AI · Accepted Answer

1. Start with the composition definition:  
   $$
   f \circ g(x) = f(g(x))
   $$

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

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

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

5. The final result is:  
   $$
   f \circ g(x) = 6x - 5
   $$
$$ f \circ g(x) = 6x - 5 $$

Upstudy AI Solution