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  4. The period of the function f(x)=a tan (π x)+x-[x] where a>0,[ . ] denotes the greatest integer function and x is a real number, is

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Q. The period of the function $ f(x)={{a}^{\{\tan (\pi x)+x-[x]\}}}, $ where $ a>0,[\,\,.\,\,] $ denotes the greatest integer function and $ x $ is a real number, is

KEAMKEAM 2007Relations and Functions - Part 2

Solution:

$ \because $ $ f(x)={{a}^{\{\tan (\pi x)+x-[x)\}}} $
$={{a}^{\{\tan (\pi x)+x\}}} $
From above it is clear that period of $ f(x) $ is 1.