Respuesta :
Solution
- The functions given are:
[tex]\begin{gathered} f(x)=3x-7 \\ g(x)=\frac{x+1}{x-1} \end{gathered}[/tex]- The solution steps are given below:
[tex]\begin{gathered} f(g(3))\text{ can be gotten by first finding the expression for} \\ f(g(x)).\text{ After this, you substitute }x=3\text{ into the expression to find }f(g(x)). \\ \\ \text{ To find }f(g(x)),\text{ we simply substitute }g(x)\text{ for }x\text{ in the expression of }f(x) \\ \\ f(x)=3x-7 \\ f(g(x))=3g(x)-7 \\ \\ \text{ But we know that:} \\ g(x)=\frac{x+1}{x-1} \\ \\ \text{ Thus, } \\ f(g(x))=3(\frac{x+1}{x-1})-7 \\ \end{gathered}[/tex]- Now that we have f(g(x)), we can substitute x = 3 to get f(g(3)). We have:
[tex]\begin{gathered} f(g(x))=3(\frac{x+1}{x-1})-7 \\ \\ put\text{ }x=3 \\ \\ f(g(3))=3(\frac{3+1}{3-1})-7 \\ \\ f(g(3))=3(\frac{4}{2})-7 \\ \\ f(g(3))=3(2)-7=6-7 \\ \\ \therefore f(g(3))=-1 \end{gathered}[/tex]Final Answer
f(g(3)) = -1
