Question

Define a function. What do you mean by the domain and range of a function? Give examples.

Answer 1

Consider A and B as two non empty sets. We know that f which associates to each element x ∈ A is a unique element which is denoted by f(x) of B is a function from A to B and we write it as

f: A → B

So the domain, co domain and range of function f: A → B where A is the domain of f, B is the codomain of f and f(A) = {f(x): x ∈ A} is the range of f.

Example:

Consider A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25}

We know that f: A → B: f(x) = x² Ɐ x ∈ A

All the elements of A has unique image in B where f is a function from A to B

By substituting the value

f(1) = 1² = 1

f(2) = 2² = 4

f(3) = 3² = 9

f(4) = 4² = 16

dom (f) = {1, 2, 3, 4} = A

codom (f) = {1, 4, 9, 16, 25} = B

range (f) = {1, 4, 9, 16}

Here, 25 ∈ B does not have pre image in A.