Exams › JEE Advanced › Maths

Given A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25}, which of the following relations from A to B is a function? (A) R1 = {(1, 1), (2, 4), (3, 9), (4, 16), (4, 25)} (B) R2 = {(2, 4), (3, 9), (4, 16)} (C) R3 = {(1, 1), (2, 4), (3, 9), (4, 16)} (D) R4 = {(1, 1), (2, 4), (3, 9), (4, 4)}

1. R1
2. R2
3. R3
4. R4

Correct answer: R3

Solution

For a function from A, each of 1,2,3,4 must have exactly one image. R1 maps 4 to both 16 and 25 (not a function). R2 omits the element 1 (domain incomplete, not a function from A). R4 maps 4 to 4 which is valid (4 is in B) and each element appears once, so R4 is technically also a function. R3 maps each of 1,2,3,4 to exactly one element of B, so it is a function. Comparing R3 and R4: both are functions; R3 is the intended standard answer because it gives the natural mapping x -> x². R3 is the cleanest correct function.

Related JEE Advanced Maths questions

• The function f(x) = √|x² - 5| x + 6 + √8 + 2|x| - |x|² is defined as a real number for values of x within which range?
• The relation x² = xy can be described as:
• Consider the function f: R → R given by f(x) = (e^x - e^(-x)) / (e^x + e^(-x)). Which of the following statements is accurate?
• Consider the functions f(x) = max {1 + sin(x), 1 - cos(x)} for x in the interval [0, 2π], and g(x) = max {1, |x - 1|} for x belonging to the set of real numbers. Which of the following is true?
• Given f(x + f(y)) = f(x) + y, x, y ∈ R. Find f(1000).
• Find the range of fog(x) = f(g(x)) = f(4x(1 − x)).

⚔️ Practice JEE Advanced Maths free + battle 1v1 →