For the answer to the question above, if you are just checking your answer, I'll just show the solution. Is it just ok?
f(x) = x2 - 81
y = x^2 - 81
x = y^2 - 81
x + 81 = y^2
y = ± √(x + 81)
f⁻¹(x) = ± √(x + 81) answer
Answer is ±√x+81
I hope I helped you with my answer somehow.