a) This is an upward parabola with vertex (-2,4)

See the attached graph.

b) since, is a parabola, (opening to the right) is not a function (since it does not pass the vertical line test). So, g(x) is not invertible.

domain of g(x) is R.

c) we have restricted the domain of f(x) such that its inverse become a function.

e) To find inverse of f(x), interchange x and y and solve for y.

d) for domain, the value inside the square root

domain of