Inverse Functions-Early answer needed

I actually don't know how to get the inverse, mathematically......maybe some other people on the site know a trick or two and could show you....!!!

Strictly speaking, we would have to have a restricted domain on the original function since it isn't one-to-one.....

However, here's what WolframAlpha has .......(the red graph is the original and the blue one is the inverse)

We would want to write it as:

f^-1(x) = (x+2)/2 ±(1/2)√(x)√(x+4)

do you actually mean

f(x)=x+(1/x)-2  

which is what you have written

OR

do you mean

f(x)=(x+1)(x-2)