Fine the domain f^-1(x)=x^2/2+2

Answer 1

y = (1/2)x^2 + 2

Swaps the vars:

x = (1/2)y^2 + 2

Solves for y

(x-2) = (1/2)y^2

2(x-2) = y^2

y = sqrt(2(x-2))

Domain:

2(x-2) >=0

2x - 4 >= 0

2x >= 4

x>=2