Relations and Functions

Let A = {1, 2, 3} and B = {4, 5}. Which of the following is a relation from A to B?

If f: R → R is defined by f(x) = 3x + 2, then f(−1) equals:

Which of the following functions is not one-to-one (injective)?

Let f: A → B and g: B → C be functions. If g ∘ f is injective, then:

Consider the relation R on set A = {1, 2, 3} defined by R = {(1,1), (2,2), (3,3), (1,2)}. Which properties does R satisfy?

If f: R → R is defined by f(x) = 1/(x − 1), what is the domain of f?

The number of functions from a set with 3 elements to a set with 2 elements is:

Let f: R → R be defined by f(x) = x² − 4x + 3. Find the range of f.

If f(x) = ax + b and g(x) = cx + d are invertible functions such that (g ∘ f)(x) = 2x + 3, then what is (f ∘ g)(x)?

Which of the following relations on set A = {1,2,3} is an equivalence relation?