Which function is an extended function

D. The last option

Explanation:

You can't divide by 0, so find out when the given function is discontinuous.

You can see that x is discontinuous at x=-1,1, so find a piecewise function that fill in those gaps.

Plug x=-1,1 into your function to find out what values you need to fill in. But of course it's discontinuous at those points, so plug in a number near x=1 and x=-1. I chose x=-1.1 and x=1.1

so we need to fill in 2 at x=-1, and fill in 4 at x=1