Question

· The period of 6x - [6x] is (where
[ ] denotes the greatest integerfunction)​

Answer 1

✪ᴀɴsᴡᴇʀ✪

• Period of $6x - 6[x]$ is 1.

᯽ᴅᴇғɪɴɪᴛɪᴏɴ᯽

A function f(x) is said to a periodic function if it repeats its value after a fix interval. Mathematically

$\to f(x + p) = f(x)$

The (smallest)fix interval, p is called the period of the function.

★ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ★

Here

$\to f(x) = 6x - 6[x]$

Let n be a positive integer, then

$\to f(x + n) = 6(x+n) - 6[x+n]$

$\to f(x + n) = 6(x+n) - 6([x] +n)$ [Since n is an Integer]

$\to f(x + n) = 6x+6n - 6[x] - 6n$

$\to f(x + n) = 6x - 6[x]$

$\to f(x + n) = f(x)$

Since $n = 1$ is the smallest positive integer satisfying the above equation, period of $f(x)$ is 1.

Thus the given function repeat as x increases by 1.