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Find the period of the following functi...

Find the period of the following functions
(i) ` f(x)=|sin 3x|`
(ii) `f(x)=2"cosec"(5x-6)+7`
(iii) ` f(x) =x-[x-2.6],` where [.] represents the greatest integer function.

Text Solution

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(i) Period of ` |sinx| " is " pi`.
So, the period of `|sin 3x| " is " (pi)/(3)`
(ii) Period of `2 "cosec"(5x-6)+7 " is " (2pi)/(5)`
(iii) `f(x) =x-[x-2.6]`
`=(x-2.6)-[x-2.6]+2.6`
`={x-2.6}+2.6,` where {.} represents fractional part function.
` :. ` Period of f(x) is '1'.
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