English
Tamil Nadu Board of Secondary EducationHSC Science Class 11

Choose the correct alternative: The function f : R → R is defined by f(x) = e(x2+cosx)(1+x4)(x-sinx)(2x-x3)+e-|x| is - Mathematics

Advertisements
Advertisements

Question

Choose the correct alternative:

The function f : R → R is defined by f(x) = `((x^2 + cos x)(1 + x^4))/((x - sin x)(2x - x^3)) + "e"^(-|x|)` is

Options

  • an odd function

  • neither an odd function nor an even function

  • an even function

  • both odd function and even function

MCQ

Solution

an even function

shaalaa.com
Functions
  Is there an error in this question or solution?
Chapter 1: Sets, Relations and Functions - Exercise 1.5 [Page 48]

APPEARS IN

Samacheer Kalvi Mathematics - Volume 1 and 2 [English] Class 11 TN Board
Chapter 1 Sets, Relations and Functions
Exercise 1.5 | Q 25 | Page 48

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"):}`


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


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

one-to-one and onto


Find the largest possible domain of the real valued function f(x) = `sqrt(4 - x^2)/sqrt(x^2 - 9)`


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


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


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 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


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


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


Choose the correct alternative:

The range of the function f(x) = |[x] − x|, x ∈ R 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:

Let X = {1, 2, 3, 4}, Y = {a, b, c, d} and f = {(1, a), (4, b), (2, c), (3, d), (2, d)}. Then f 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×