Relation and Function
NCERT Exemplar Problem
Short Answer Type
Question 1: Let A = {a, b, c} and the relation R be defined on A as follows:
R = {(a, a), (b, c), (a, b)}.
Then, write minimum number of ordered pairs to be added in R to make R reflexive and transitive.
Solution: In order to make R reflexive, (b, b) and (c, c) will be added to R.
And in order to make R transitive, (a, c) will be added to R.
Therefore, The minimum number of order pair to be added to R will be (b, b), (c, c) and (a, c) - Answer
Question 2: Let D be the domain of real valued function f defined by
then, write D.
Solution: Here given D is the domain of
Therefore,
Therefore, D = [– 5, 5] - Answer
Question 3: 
be defined by 
respectively. Then find g o f.
Solution:
Question 4:
be the function defined by
Solution:
Question 5: If A = {a, b, c, d} and the function f = {(a, b), (b, d), (c, a), (d, c)}, write f – 1
Solution: Given, f = {(a, b), (b, d), (c, a), (d, c)}
Therefore, f – 1 ={(b, a), (d, b), (c, a), (c, d)} Answer
Question 6: If
is defined by
Solution: Given,
Question 7: Is g = {(1, 1), (2, 3, (3, 5), (4, 7)} a function? If g is described by g(x) = αx + β, then what value should be assigned to α and β?
Solution: Given, g = {(1, 1), (2, 3, (3, 5), (4, 7)}
Therefore, each of the element of domain will be have unique image.
Consequently, g is a function.
Now, after substituting the value of α in equation (i), we get
