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High School Mathematics - 2
4.3 Identity, Constant and Equal Functions

Constant Function
A function f: A ->B is called a constant function if every element of A is associated with the same element of B, i.e the range of f consists of only one element as shown.

Example: Let A = {2,3,5,7,11} and B = {0,7,14, 21}, then f = {(2,0), (3,0), (5,0),(7,0), (11,0)} is a constant function.

Identity Function
Let A be any set. A function f: A ->A is called an identity function if for every x A,f(x) = x. i.e if every element is mapped onto itself. It is denoted as IA. Then IA(x) = x for all x A.

Example: Let A = {1,2,3,4}, then f = {(1,1), (2,2), (3,3), (4,4) } is an identity function.

Equal Function
Two functions f and g are said to be equal written as f = g if they have the same domain and they satisfy the condition f(x) = g(x) for all x.
Example: Consider function f defined as shown below in the diagram

let a function g be defined by the formula g(x) = x2 where the domain of g is {1,2}. Then f = g since they both have the same domain and since f and g both assign the same image to each element in the domain.


Directions: Answer the following.
Q 1:
Answer:

Q 2:
Answer:

Q 3: Let f: A -> B and g: B -> C be two functions, and f and g both are one-to-one, then gof is ____.
one-one
constant
onto

Q 4: If every element is mapped to itself then it is ____ function.
Equal
Constant
Identity

Q 5:
Answer:

Q 6:
Answer:

Q 7:
Answer:

Q 8: A function f: A -> B is called a ____ function, if all elements in A is mapped to the same element in B.
constant
constant
identity

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Question 10: This question is available to subscribers only!


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