RELATIONS AND FUNCTIONS CLASS 11 WORKSHEET

(1)  Suppose that 120 students are studying in 4 sections of eleventh standard in a school. Let A denote the set of students and B denote the set of the sections. Define a relation from A to B as “x related to y if the student x belongs to the section y”. Is this relation a function? What can you say about the inverse relation? Explain your answer.              Solution

(2)  Write the values of f at −4, 1,−2, 7, 0 if

Solution

(3)  Write the values of f at −3, 5, 2,−1, 0 if

Solution

Question 4 :

If

A = {1, 2, 3} 

and let

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

then R is:

(a) Reflexive, symmetric but not transitive

(b) symmetric, transitive but not reflexive

(c) Reflexive and transitive but not symmetric

(d) an equivalence relation

Question 5 :

Let R be a relation defined on Z by a R b <=> a ≥ b, then R is:

(a) symmetric, transitive but not reflexive

(b) Reflexive, symmetric but not transitive

(c) Reflexive and transitive but not symmetric

(d) an equivalence relation

Question 6 :

Let R be a relation defined on Z as follows: (a, b) ∈ R <=> a² + b² = 25, then domain of R is:

(a) {3, 4, 5}     (b) {0, 3, 4, 5}     (c) {0, ± 3, ±4, ±5}

(d) none of these

Problem 1 :

State whether the following relations are functions or not. If it is a function check for one-tooneness and ontoness. If it is not a function, state why?

If A = {a, b, c} and f = {(a, c), (b, c), (c, b)}; (f : A → A).

Problem 2 :

If X = {x, y, z} and f = {(x, y), (x, z), (z, x)}; (f : X → X).           Solution

Problem 3 :

Let A = {1, 2, 3, 4} and B = {a, b, c, d}.

Give a function from A → B for each of the following:

(i) neither one-to-one nor onto.

(ii) not one-to-one but onto.

(iii) one-to-one but not onto.

(iv) one-to-one and onto.

Solution

Determine if the following relations are functions. Then state the domain and range.

Problem 4 :

{(1, -2) (-2, 0) (-1, 2) (1, 3)}

Solution

Problem 5 :

{(1, 1) (2, 2) (3, 5) (4, 10)(5, 15)}

Solution

Write each of the following as relation, state the domain and range and determine if it is function or not.

Problem 6 :

Solution

Problem 7 :

Solution

Problem 8 :

Rewrite the relation given in the mapping diagram as a scatterplot.

Is the relation also a function?

Solution

Problem 9 :

Rewrite the relation given in the scatter plot as a mapping diagram.

Is the relation also a function?

Solution

Determine if each graph shows a function or a relation only. Then identify the domain and range.

Problem 10 :

Solution

Problem 11 :

Solution

Problem 12 :

Solution

Question 1 :

Find the domain of 1 / (1 − 2 sinx) 

Solution

Question 2 :

Find the largest possible domain of the real valued function f(x)  =  √(4 - x²)/ √(x² - 9)

 Solution

Question 3 :

Find the range of the function

1 / (2 cos x − 1)

Solution

Question 4 :

Show that the relation xy = −2 is a function for a suitable domain. Find the domain and the range of the function.

Solution

Question 5 :

Find domain and range of the following real valued functions:

i) f(x) = |𝑥| + 1

ii) f(x) = √(27 − x²)

iii) f (x) = 𝑥² / (𝑥² + 1)

iv) –|x + 2|

Solution

Question 6 :

Find the domain and range of

(x² + 5x - 6) / (x² - 3x + 2)

Solution

Problem 1 :

The total cost of airfare on a given route is comprised of the base cost C and the fuel surcharge S in rupee. Both C and S are functions of the mileage m; C(m) = 0.4m + 50 and S(m) = 0.03m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles.

Solution

Problem 2 :

A salesperson whose annual earnings can be represented by the function A(x) = 30, 000 + 0.04x, where x is the rupee value of the merchandise he sells. His son is also in sales and his earnings are represented by the function S(x) = 25, 000 + 0.05x. Find (A + S)(x) and determine the total family income if they each sell Rupees 1, 50, 00, 000 worth of merchandise.

Solution

Problem 3 :

The function for exchanging American dollars for Singapore Dollar on a given day is f(x) = 1.23x, where x represents the number of American dollars. On the same day the function for exchanging Singapore Dollar to Indian Rupee is g(y) = 50.50y, where y represents the number of Singapore dollars. Write a function which will give the exchange rate of American dollars in terms of Indian rupee.

Solution

Problem 4 :

The owner of a small restaurant can prepare a particular meal at a cost of Rupees 100. He estimates that if the menu price of the meal is x rupees, then the number of customers who will order that meal at that price in an evening is given by the function D(x) = 200−x. Express his day revenue, total cost and profit on this meal as functions of x.

Solution

Problem 5 :

The formula for converting from Fahrenheit to Celsius temperatures is y = (5x/9) − (160/9). Find the inverse of this function and determine whether the inverse is also a function

Solution

Problem 6 :

A simple cipher takes a number and codes it, using the function f(x) = 3x−4. Find the inverse of this function, determine whether the inverse is also a function and verify the symmetrical property about the line y = x (by drawing the lines).

Solution

Problem 7 :

f(x) = x² + 2x + 1

show that f(x + 2) - f(x) = 4x + 8

Solution

Problem 8 :

The function f is such that f(x) = kx + 3

The function g is such that g(x) = 2x - 4

Given that gf(2) = 34

Work out the value of k

Solution

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