हिंदी
तमिलनाडु बोर्ड ऑफ सेकेंडरी एज्युकेशनएचएससी विज्ञान कक्षा ११

Choose the correct alternative: The function f : R → R is defined by f(x) = sin x + cos x is - Mathematics

Advertisements
Advertisements

प्रश्न

Choose the correct alternative:

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

विकल्प

  • an odd function

  • neither an odd function nor an even function

  • an even function

  • both odd function and even function

MCQ

उत्तर

neither an odd function nor an even function

shaalaa.com
Functions
  क्या इस प्रश्न या उत्तर में कोई त्रुटि है?
अध्याय 1: Sets, Relations and Functions - Exercise 1.5 [पृष्ठ ४८]

APPEARS IN

सामाचीर कलवी Mathematics - Volume 1 and 2 [English] Class 11 TN Board
अध्याय 1 Sets, Relations and Functions
Exercise 1.5 | Q 24 | पृष्ठ ४८

संबंधित प्रश्न

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

f(x) = `{{:(- x + 4,  "if" - ∞ < x ≤ - 3),(x + 4,  "if" - 3 < x < -2),(x^2 - x,  "if" - 2 ≤ x < 1),(x - x^2,  "if"  1 ≤ x < 7),(0,  "otherwise"):}`


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:

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 and onto


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


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 distance of an object falling is a function of time t and can be expressed as s(t) = −16t2. Graph the function and determine if it is one-to-one.


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


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


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)


Choose the correct alternative:

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


Choose the correct alternative:

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


Choose the correct alternative:

If the function f : [−3, 3] → S defined by f(x) = x2 is onto, then S 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


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×