The period of the function $f(x) = a^{\left\{ an(\pi x) + x - \lbrack x brack ight\}}$, where $a 0$, [image:2_image4.emf] denotes the greatest integer function and $x$ is a real number, is

Question

The period of the function $f(x) = a^{\left\{ 	an(\pi x) + x - \lbrack xbrack ight\}}$, where $a > 0$, [image:2_image4.emf] denotes the greatest integer function and $x$ is a real number, is

Dr. Abubacker · Accepted Answer

(d)
$\because\ \ f(x) = a^{\left\{ 	an{(\pi x) + x - \lbrack xbrack} ight\}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \  = a^{\left\{ 	an{(\pi x) + (x)} ight\}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \  = a^{	an{\pi x}}a^{\left\{ x ight\}}$
Hence, period of $f(x)$ is 1.

Q. The period of the function $f(x) = a^{\left\{ \tan(\pi x) + x - \lbrack x\rbrack \right\}}$, where $a > 0$,

denotes the greatest integer function and $x$ is a real number, is

Explanation

Reviewed by Dr. Abubacker

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

Explanation

Reviewed by Dr. Abubacker

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Q. The period of the function $f(x) = a^{\left\{ \tan(\pi x) + x - \lbrack x\rbrack \right\}}$, where $a > 0$,

denotes the greatest integer function and $x$ is a real number, is