CLASS-11
RELATION & FUNCTION - DEFINITION OF FUNCTION

DEFINITION OF FUNCTION -

Definition – A function is a is a special type of relation in which no two different ordered pairs have the same first component.

Stated directly in terms of a set of ordered pairs, the definition is as given below.

Definition – A function is a set of ordered pairs, no two of which have the same first components.

Stated directly in terms of a set of ordered pairs, the definition is as given below –

Definition – A function is a set of ordered pairs, no two of which have the same first components. The set {(0, 1), (1, 1)} is a function but the set {(1, 0), (1, 1)} is not a function as first component is repeated

A function is usually denoted by f, g, h, F, G, H

Math Alert – By convention, the empty set is not considered a function. A function is usually denoted by letters f, g, F, G.

Thus, here, f = {(a, 1), (b, 2), (c, 3), (d, 3)}

Range (f) ⊆ co-domain (f)