Given f(x) = (x-2)^2 + 1...?

Question

a) what are the sets of domain f, codomain f and range F?
b) Find the largest subset of domain f so that F is restricted to that set is injective.
c)What is F inverse?

Answer 1

a) Domain: (-infinity, infinity)
Range/Codomain: [0, infinity)
b) Largest subset of f, so that F is injective: [0, infinity)
c) f inverse:
x = 2 + (y - 1) ^ .5

Answer 2

For (a), the domain is all real numbers. x can take on any real value. For any real value of x, (x - 2)^2 will be positive or zero, so the range is +1 to infinity.