But sqrt · square = 1, where "sqrt: R⁺ → R⁺" is the square root operation, "square: R⁺ → R⁺" is the squaring operation, "1: R⁺ → R⁺" is the identity operation, and (·) is function composition: i.e., working in the monoid of functions R⁺ → R⁺. So x² and sqrt(x), as elements of R, are not inverses, but sqrt and square, as elements of R⁺ → R⁺, are.
It depends on how you parse the phrase "fast inverse square root".
This is true, but interpreting it one way is clearly absurd (nobody would call a square the “inverse square root”), which implicates that the other meaning was intended.
It depends on how you parse the phrase "fast inverse square root".