Question

How do you find the inverse of `f(x) = x – 7` and is it a function?

Answer 1

The inverse function is `f^-1(x)=x+7`

Explanation:

To find the inverse function of `y=f(x)` you have to calculate `x` as function of `y` and check if the formulka you get describes a function i. e. it has only one possible value for any argument.

In this example our function is `y=x-7`.

`y=x-7`

`y-x=-7`

`-x=-y-7`

`x=y+7`

It is a function. For any number `x` there is only one number `7` greater than `x`, so there is only one value.

Now we can write the inverse function using standard notation (x# for argument and `y` for value).

The inverse is `y=x+7`