Functions

Question 1

What is a function?

Answer 1

A function is a type of relation which relates one input to exactly one output.

Question 2

What is a domain?

Answer 2

A domain is the set of possible input values of a function.

Question 3

What is the codomain?

Answer 3

A codomain is the set of possible output values a function can produce.

Question 4

What is the range of a function?

Answer 4

The range of a function is a subset of its codomain; it is the set of values the function actually produces.

Question 5

What is an injective function?

Answer 5

A function f: X→Y is said to be injective if and only if whenever f(x) = f(x₁), x₁ = x₂. This means that no two distinct element in X can be mapped to the same element in Y.

A function f: X →Y is injective if for all x₁, x₂ ∈ X, there exists y₁ y₂ ∈ Y such that f(x₁) = y₁,
and f(x₂) = y₂

Question 6

What is a surjective function?

Answer 6

A function f:X→Y is surjective if and only if for every element in Y, there exists at least one element in X such that f(x) = y. This implies that, unlike injective functions, distinct elements in X can be mapped to the same elements in Y.

Question 7

What is a bijective function?

Answer 7

A function f: X→Y is bijective if and only if for every element in Y there exists only one element in X such that f(x) = y. It is also called a one-to-one and onto function.