Question

Given `H = x^2 + 8`, what is `H^-1`?

Answer 1

The notation `H^-1` means the inverse function. The equation of the inverse function can be found by switching the `x` and `y` values inside the function.

`y = x^2 + 8`

`x = y^2 + 8`

`x - 8 = y^2`

`y = +-sqrt(x - 8)`

Hence, `H^-1(x) = +-sqrt(x- 8)`.

Hopefully this helps!