The function h is defined by h(x)= x^2-2. for x is less than or equal to 0.Find an expression for h^-1(x)

Expert Answers
lemjay eNotes educator| Certified Educator

The given function is:

`h(x)=x^2 -2 `     for `xlt=0` .

To determine its inverse `h^(-1)(x)` , replace h(x) with y.


Then, switch x and y.

`x=y^2 -2`

And, solve for y. To do so, add both sides by 2.



Take the square root of both sides.





Then, replace y with `h^(-1)(x)` .


But,  consider the given domain of the the function h(x).

The domain  of h(x) is `xlt=0` . This indicates that the range of the inverse function is `ylt=0` .

Then, `h^(-1)(x)` take only the negative y.

Hence, the inverse function of `h(x)=x^2-2` for `xlt=0` is `h^(-1)(x) = -sqrt(x+2)` .