## Kerala Plus One Maths Chapter Wise Previous Questions and Answers Chapter 2 Relations and Functions

Question 1.

Consider the following graphs:

a. Which graph does not represent a function?

b. Identify the function from the above graphs.

c. Draw the graph of the function [March-2018]

Answer:

a. (b) or(c)

b. (a)

c.

Question 2.

The figure shows the graph of a function f(x) which is a semi circle centred at origin.

a. Write the domain and range of f(x).

b. Define the function f(x). [March-2018]

Answer:

Question 3.

a. The domain of the function is ……….

i. {1}

ii. R

iii.R- {1}

iv. R- {0}

b. A relation R on the set of natural numbers is defined by R = {(x,y): y= x+5;x is a natural number less than 4, x, y ∈N}.

i. Write the relation in Roster form

ii. Write the domain and range of the relation.

c. Draw the graph of the function

f(x) = |x|,x∈R. [March-2017]

Answer:

Question 4.

a. If (x+1, y-2) = (3,1), write the values of x and y. [March-2016]

b. Let A={1,2,3,4,5} and B={4,6,9} be two sets. Define a relation R from A to B by R={(x, y): x-y is a positive integer}.

Find A × B and hence write R in the Roster form.

c. Define the modulus function. What is its domain? Draw a rough sketch.

Answer:

a. (x+1, y-2) = (3,1)

x+1=3; x=2

y-2 = 1; y = 3

b. A×B = { (1,4),( 1,6),( 1,9), (2,4), (2,6),(2,9),(3,4), (3,6), (3,9), (4,4), (4,6) ,(4,9),(5,6), (5,9)}

R = x-y is a positive integer R ={(5,4)}

c. A real function R is to be a modulus function, if f (x) = |x|, x∈R, is known as modulus function.

Domain =R

Question 5.

a. Find the domain of the function

a. Sketch the graph of the function f(x) = |x+1|.

b. Consider A= {1,2,3,5} and B = {4,6,9}. Define a relation R: A→B by

R = {(x,y): x – y is odd, x ∈ A, y∈ B}. Write R in roster form and find the range of R. [March-2015]

Answer:

a. x^{2} – 5x + 4 = 0

(x – 4) (x -1) = 0

x = 4,x=1

f (x) is defined for all real numbers except 4 and l.D_{f }=R-{1,4}

c. A × B = {(1,4), (1,6), (1,9), (2,4), (2,6), (2,9), (3,4), (3,6), (3,9), (5,4), (5,6), (5,9)}

R= {(1,4), (1,6), (2,9), (3,4), (3,6), (5,4), (5,6)}

Range ={4,6,9}

Question 6.

a. Let P= {1,2}. Find P× P× P.

b. Let A = {1,2, 3,……………… , 13,14}.R is the relation on A defined by R = {(x,y):

3x – y = 0 ; x, y∈A}

i. Write R in a tabular form.

ii. Find the domain and range of R. [March-2014]

Answer:

a. P × P × P = {(1,1,1) (1,1,2) (1,2,1)(1,2,2) (2,1,1 ),(2,1,2),(2,2,1), (2,2,2)}

b. A={ 1,2,3……………… 13,14}

R= {(x,y): 3x-y = 0; x, y e A}

i. R – {(x,y): difference between 3x and y is zero, x, y∈ A}

R= {(1,3), (2,6), (3,9), (4,12)}

ii. Domain = {1,2,3,4}

Range = {3,6,9,12}

Question 7.

a. Let A={7,8}, B={5,4,2} Find A× B.

b. Determine the domain and range of relation R defined by R={(x,y):y = x + 1, x ∈{0,1,2,3,4,5}} [March-2013]

Answer:

a. A= {7,8} and B = {5,4,2}

A × B = {(7,5), (7,4), (7,2), (8,5), (8,4), (8,2)}

b. Domain={0,1,2,3,4,5}

Range={1,2,3,4,5,6}

R= {(0,1), (1,2), (2,3), (3,4),(4,5), (5,6)}

Question 8.

Draw the graph of the function f (x) = |x| + 1, x∈R. [March-2013]

Answer:

Question 9.

i. If A = {1, 2} and B = {3, 4}, write the number of relations from A and B.

ii. Determine the domain and range of the relation R, where R = {(x, x^{3}): x is prime number <15}

iii. Draw the graph of Signum function. [February-2013]

Answer:

i. A = {1, 2} and B = {3, 4} there are 2^{mn }relations, i.e., 2^{4} = 16 relations

ii. R= {(2,8), (3,27), (5,125),(7,342),(11,1331), (13,2197)}

Domain = (2,3,5,7,11,13)

Range = (8,27,125,342,1331,2197)

iii.

Question 10.

Let A= {1,2,3,4,5} and R be a relation on A defined by R={(a,b):b = a^{2}}

a. Write R in the roster form,

b. Find the Range of R. [March-2012]

Answer:

a. R = {(1,1), (2,4)}

b. Range of R= {1,4}

Question 11.

Consider the real function

a Find the Domain and Range of the function.

b. Prove that f (x) f (-x) + f(0) = 0 [March-2012]

Answer:

Question 12.

Let A= {1,2,3,4,6} and R be a relation on A defined by R = {(a,b): a,b ∈ A,b is exactly divisible by a}

i. Write R in the roster form.

ii. Find the domain and range of R. [March-2011]

Answer:

i.R = (1,1)(1, 2)(1, 3)(1,4)(1, 6)(2, 2) (2,6)(3,3)}

ii. Domain= {1,2,3,4,6}

Range = {1,2, 3,4, 6}

Question 13.

Consider the real function

i. Find the value of x if f(x) = 1.

ii. Find the domain of f [March-2011]

Answer:

Question 14.

Consider the relation R = {(x, 2x – 1/x e A) where A={2, -1,3}}

i. Write R in roster form.

ii. Write the range of R. [March-2010]

Answer:

R= {(2,3), (-1,-3) (3,5)}

ii. Range = {3,-3,5}

Question 15.

Consider the function

.find

i. Domain of ‘f’.

ii.Domain of ‘g’

iii.(f+g) (x)

iv. (fg) (x)

Answer:

i. Domain of‘F = {x∈R: x≥2}

ii. Domain of ‘g’= R – {1}

iii. (f+g)(x) = f(x) + g(x)

Question 16.

The cartesian product P x P has 9 elements among which are found (-a, 0) and (0, a). A relation from P to P defined as R={(x, v): x+y=0}

a. Find P.

b. Depict the relation using an arrow diagram.

c. Write down the domain and range of R.

d How many relations are possible from P to P? [September-2010]

Answer:

a.P={-a,0,a}

c. Domain =Range ={-a,0,a}

d. n(P×P) = 9

Possible number of relations from P to OP=2^{9}

Question 17.

Let A= {1,2,3,…., 14}. R is a relation on A defined by R = {(x, y): 3x – y = 0, x, y ∈ A}

i. Write R in tabular form

ii. Find the domain and range of R. [August-2009]

Answer:

i. R= {(1,3), (2,6), (3,9), (4,12)}

ii. Domain= {1,2,3,4}, Range = {3,6,9,12}

Question 18.

Consider the function f (x) =2 – 3x, x ∈ R, x ≥ 0

i. Find its range.

ii. Draw its graph in the given domain. [August-2009]

Answer:

i.Range = (-∞, 2]

Question 19.

LetA= {1,2},B= {3,4}

a. Choose the number of relations from A to B from the bracket: [4,16,32,64]

b. Determine the domain and range of the relation R,

where R={(x, x^{3}): x is a prime number less than 15}.

c. From the below graph, write the name and equation of the function. [March-2009]

Answer: