Question

Find f^{-1}(x) for the function below. Do not put spaces between your characters. If no inverse exists then type "none".f(x)=x+5f^{-1}(x)=Answer

Answer 1

`f^(-1)(x)=x-5`

1) To find out the inverse function of a function we need to swap the variables, and then isolate the y variable on the left, like this:

`\begin{gathered} f(x)=x+5 \\ y=x+5 \\ x=y+5 \\ x-y=y-y+5 \\ x-y=5 \\ -x+x-y=5-x \\ -y=5-x \\ y=x-5 \\ f^(-1)(x)=x-5 \end{gathered}`

Note that after that, we can isolate and then divide the whole function by -1

2) Hence, the answer is:

`f^(-1)(x)=x-5`