Advertisements
Advertisements
Question
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)
Advertisements
Solution
X = {x, y, z}
f = {(x, y), (x, z), (z, x)} f : X → X
The relation f : X → X is not a function since the element x in the domain has two images in the co-domain.
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"):}`
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 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, 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
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 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 `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 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
