Relations and Functions

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

Which of the following is a function from set A = {1, 2, 3} to B = {a, b} ?

If f: R → R is defined by f(x) = 2x + 3, what is f(−2)?

If f: A → B and g: B → C are functions, then the composition g ∘ f is a function from:

Let f: R → R be defined by f(x) = x². Is f one-one and onto?

If a relation R on set A is symmetric and transitive, which additional property must it have to be an equivalence relation?

Given f: R → R defined by f(x) = (x − 1)/(x + 1), find f⁻¹(x) (the inverse function).

If f: A → B is onto and g: B → C is onto, then g ∘ f: A → C is:

Let f: R → R be defined by f(x) = 3x + 5. Find the value of (f ∘ f)(x).

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