English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative: The function f : [0, 2π] → [−1, 1] defined by f(x) = sin x is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

The function f : [0, 2π] → [−1, 1] defined by f(x) = sin x is

Options

  • one-to-one

  • onto

  • bijection

  • cannot be defined

MCQ

Solution

onto

shaalaa.com
Functions
  Is there an error in this question or solution?
Chapter 1: Sets, Relations and Functions - Exercise 1.5 [Page 47]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 1 Sets, Relations and Functions
Exercise 1.5 | Q 19 | Page 47

RELATED QUESTIONS

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


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

f(x) = `{{:(x^2 + x - 5,  "if"  x ∈ (−∞, 0)),(x^2 + 3x - 2,  "if"  x ∈ (3, ∞)),(x^2,  "if"  x ∈ (0",", 2)),(x^2 - 3,  "otherwise"):}`


State whether the following relations are functions or not. If it is a function check for one-to-oneness 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)


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

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


Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

neither one-to-one nor onto


Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

not one-to-one but onto


Let A = {1, 2, 3, 4} and B = {a, b, c, d}. Give a function from A → B of the following:

one-to-one but not onto


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


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


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


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) = 0.4 m + 50 and S(m) = 0.03 m. Determine a function for the total cost of a ticket in terms of the mileage and find the airfare for flying 1600 miles


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


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


Choose the correct alternative:

If f(x) = |x − 2| + |x + 2|, x ∈ R, then


Choose the correct alternative:

The range of the function  `1/(1 - 2 sin x)` is


Choose the correct alternative:

The number of constant functions from a set containing m elements to a set containing n elements is


Choose the correct alternative:

The inverse of f(x) = `{{:(x,  "if"  x < 1),(x^2,  "if"  1 ≤ x ≤ 4),(8sqrt(x),  "if"  x > 4):}` is


Choose the correct alternative:

The function f : R → R is defined by f(x) = sin x + cos x is


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×