Advertisements
Advertisements
Question
Choose the correct alternative:
The function f : R → R is defined by f(x) = sin x + cos x is
Options
an odd function
neither an odd function nor an even function
an even function
both odd function and even function
Solution
neither an odd function nor an even function
APPEARS IN
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 − 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"):}`
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
Find the domain of `1/(1 - 2sinx)`
Find the largest possible domain of the real valued function f(x) = `sqrt(4 - x^2)/sqrt(x^2 - 9)`
Find the range of the function `1/(2 cos x - 1)`
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
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 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
