Any insight on how to solve this problem will be greatly appreciated.

Question

Find the inverse of f(x)=|x-3|. State whether or not the inverse is a function. If it is not, what do we need to do to make it a function.

Answer 1

To determine if a relation is a function, it has to pass the vertical line test, which it does. To determine if it has an inverse, it has to pass the horizontal line test. This is V shaped, it does not pass the horizontal line test, so it does not have an inverse. To make it have an inverse, you have to restrict the domain. In this case you could restrict the domain so x≥3. This would be half of the V shape, so it would have an inverse that is a function.