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
Advertisements
Solution
neither an odd function nor an even function
APPEARS IN
RELATED QUESTIONS
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)
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
Find the domain of `1/(1 - 2sinx)`
Find the range of the function `1/(2 cos x - 1)`
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
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
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:
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 function f : [0, 2π] → [−1, 1] defined by f(x) = sin x 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
