Given f(x)=x+1; g(x)=√x-2; h(x)=2/x Perform the indicated operations and supply the domain and range of the resulting function: h^-1

Expert Answers
rcmath eNotes educator| Certified Educator

To find the inverse function we write y=2/x and solve for x.

`y=2/x=>xy=2=>x=2/y`

Hence the inverse function is `h^(-1)(x)=2/x`

The domain is D=`(-oo,0)U(0,oo)`

The function can never be equal zero, so R=`(-oo,0)U(0,oo)`

The following graph help explain why the function and its inverse are the same.