# RELATIONS AND FUNCTIONS CLASS 11 WORKSHEETS

## About "Relations And Functions Class 11 Worksheets"

Relations And Functions Class 11 Worksheets

Here we are going to see some practice questions on relations and functions.

(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

(4)  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?

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

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

(5)  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

(6)  Find the domain of 1 / (1 − 2 sinx)        Solution

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

(8) Find the range of the function

1 / (2 cos x − 1)

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

(10)  If f, g : R → R are defined by f(x) = |x| + x and g(x) = |x| − x, find g ◦ f and f ◦ g.         Solution

(11)  If f, g, h are real valued functions defined on R, then prove that (f + g) ◦ h = f◦h + g ◦ h. What can you say about f ◦ (g + h) ? Justify your answer.       Solution

(12)  If f : R → R is defined by f(x) = 3x − 5, prove that f is a bijection and find its inverse.       Solution

(13)  The weight of the muscles of a man is a function of his body weight x and can be expressed as W(x) = 0.35x. Determine the domain of this function.       Solution

(14)  The distance of an object falling is a function of time t and can be expressed as s(t) = −16t2Graph the function and determine if it is one-to-one.       Solution

(15)  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

(16)  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

(17)  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

(18)  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

(19)  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

(20)  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

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WORD PROBLEMS

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Graphing rational functions

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Decimal representation of rational numbers

Finding square root using long division

L.C.M method to solve time and work problems

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