Given ##H = x^2 + 8##, what is ##H^-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!