Question

Consider these functions:f(x) = 3x - 7g(x)= x+1 /x-1What is the value of f(g(3))?

Answer 1

- The functions given are:

`\begin{gathered} f(x)=3x-7 \\ g(x)=(x+1)/(x-1) \end{gathered}`

- The solution steps are given below:

`\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)=(x+1)/(x-1) \\ \\ \text{ Thus, } \\ f(g(x))=3((x+1)/(x-1))-7 \\ \end{gathered}`

- Now that we have f(g(x)), we can substitute x = 3 to get f(g(3)). We have:

`\begin{gathered} f(g(x))=3((x+1)/(x-1))-7 \\ \\ put\text{ }x=3 \\ \\ f(g(3))=3((3+1)/(3-1))-7 \\ \\ f(g(3))=3((4)/(2))-7 \\ \\ f(g(3))=3(2)-7=6-7 \\ \\ \therefore f(g(3))=-1 \end{gathered}`

Final Answer

f(g(3)) = -1