Advertisements
Advertisements
प्रश्न
Choose the correct alternative:
The function f : [0, 2π] → [−1, 1] defined by f(x) = sin x is
पर्याय
one-to-one
onto
bijection
cannot be defined
उत्तर
onto
APPEARS IN
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"):}`
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:
one-to-one and 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)`
If f, g : R → R are defined by f(x) = |x| + x and g(x) = |x| – x find g o f and f o g
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 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 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:
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 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:
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
Choose the correct alternative:
The function f : R → R is defined by f(x) = sin x + cos x is
