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Period of a Function

Period of a f...

Question

Period of a function is always a positive integer.

A

True

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B

False

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Solution

The correct option is B
False

A function f : $X \to Y$ is said to be a periodic function if there exists a positive real number p such that f(x +p) = f(x), for all x € X. We call this value p as the period of the functions. From the definition, it is clear that p can be any positive real number, not just positive integers. If you are familiar with period of standard functions, you will see that the period of sinx, is an irrational number, not an integer.

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(i) The smallest integer is zero.
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(i) The sum of two negative integers is always a negative integer.
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(iii) The sum of an integer and its negative is zero.
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Q. State true or false.
(i) The product of a negative and a positive integer may be zero.
(ii) The product of two negative integers is always positive.
(iii) The product of two integers with opposite signs is the same as the product of their absolute values.
(iv) If exactly one of the three given integers is negative, then product is always negative.
(v) The product of any two positive or any two negative integers is always smaller than the integers.

Question 90

State whether the statement is True or False.

Product of a negative integer and a positive integer is a positive integer.

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