Question:
Which of the following functions is periodic?
Which of the following functions is periodic?
Updated On: Jun 14, 2022
- f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x
- $f(x) = \sin \frac{1}{x}$ for $x \neq 0, f(0) = 0$
- $f(x) = x \cos x$
- none of these
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The Correct Option is A
Solution and Explanation
Answer (a) f(x) = x - [x] where [x] denotes the largest integer less than or equal to the real number x
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Concepts Used:
Relations and functions
A relation R from a non-empty set B is a subset of the cartesian product A × B. The subset is derived by describing a relationship between the first element and the second element of the ordered pairs in A × B.
A relation f from a set A to a set B is said to be a function if every element of set A has one and only one image in set B. In other words, no two distinct elements of B have the same pre-image.
Representation of Relation and Function
Relations and functions can be represented in different forms such as arrow representation, algebraic form, set-builder form, graphically, roster form, and tabular form. Define a function f: A = {1, 2, 3} → B = {1, 4, 9} such that f(1) = 1, f(2) = 4, f(3) = 9. Now, represent this function in different forms.
- Set-builder form - {(x, y): f(x) = y2, x ∈ A, y ∈ B}
- Roster form - {(1, 1), (2, 4), (3, 9)}
- Arrow Representation
