The period of the function f(x)=a tan (π x)+x-[x] where a0,[ . ] denotes the greatest integer function and x is a real number, is

Question

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 (A)  π  (B)  π /2  (C)  π /4  (D)  2π

Tardigrade Admin · Accepted Answer

∵ f(x)=a tan (π x)+x-[x) =a tan (π x)+x From above it is clear that period of f(x) is 1.

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

$π$

$π /2$

$π /4$

$2 π$

1

$∵$ $f (x) = a^{{t a n (π x) + x - [x)}}$
$= a^{{t a n (π x) + x}}$
From above it is clear that period of $f (x)$ is 1.

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

π

π/2

π/4

2π

1

∵ f(x)=a{tan(πx)+x−[x)} =a{tan(πx)+x} From above it is clear that period of f(x) is 1.

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

$π$

$π /2$

$π /4$

$2 π$

$∵$ $f (x) = a^{{t a n (π x) + x - [x)}}$
$= a^{{t a n (π x) + x}}$
From above it is clear that period of $f (x)$ is 1.