f(x)'s domain is the extent of its x-values and the function x^2 + 3 extends to infinity and negative infinity so its domain is all real #s,
f(x)'s range is its y-values and f(x) is only defined for and values above 3, so its range is y>= 3
f(x)^-1 is the function (x-3)^(1/2) which is a square root function and x >= 3 because if x were to be 2 there would be a negative in the square root which means the y-value would be on the imaginary axis.
the range is y>= 0 because the output of the square root function can never be negative in this context as it is not being multiplied by a negative on the front