Question

12. Let f(x) = 12x + 4. Find f(f^-1(x)). Show your work.Is this what you expected to find? Why or why not

Answer 1

We want to find f(f^-1(x)), for that we first need to find the inverse of the function, which is f^-1(x). This is done step-by-step below:

`\begin{gathered} y\text{ = 12x+4} \\ x\text{ = 12y+4} \\ x-4=12y \\ 12y=x-4 \\ y=(x-4)/(12) \\ f^(-1)(x)=(x-4)/(12) \end{gathered}`

We have to use the value of f^-1(x) as the input of f(x).

`\begin{gathered} f(f^(-1)(x))\text{ = 12}\cdot((x-4))/(12)+4 \\ f(f^(-1)(x))\text{ = x-4 + 4} \\ f(f^(-1)(x))\text{ = x} \end{gathered}`