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

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UpStudy AI · Accepted Answer

1. We start with the definition of a composition of functions:  
   $$
   (f \circ g)(x) = f(g(x))
   $$

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

3. The function $$ f(x) $$ is given by $$ f(x) = 3x + 4 $$. Replace $$ x $$ with $$ 2x - 3 $$ in this expression:  
   $$
   f(2x - 3) = 3(2x - 3) + 4
   $$

4. Distribute the 3:  
   $$
   3(2x - 3) = 6x - 9
   $$

5. Add the 4:  
   $$
   6x - 9 + 4 = 6x - 5
   $$

6. Therefore, the composition $$ f \circ g(x) $$ 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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