let f x nx n nx n tan pi x2 where x is the greatest integer

Let $$f\left( x \right) = nx + n - \left[ {nx + n} \right] + \tan \frac{{\pi x}}{2},$$ where $$\left[ x \right]$$ is the greatest integer $$ \leqslant x$$ and $$n\, \in \,N.$$ It is :

A. a periodic function of period 1

B. a periodic function of period 4

C. not periodic

D. a periodic function of period 2

Answer : a periodic function of period 2

Solution :
$$nx + n - \left[ {nx + n} \right]$$ has the period 1 and $$\tan \frac{{\pi x}}{2}$$ has the period $$\frac{\pi }{{\frac{\pi }{2}}}$$ i.e., 2.
LCM of 1, 2 is 2.

Releted MCQ Question on
Calculus >> Function

Releted Question 1

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

A. Injective but not surjective

B. Surjective but not injective

C. Bijective

D. None of these.

View Answer

Releted Question 2

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

A. $$k < 7$$

B. $$ - 5 < k < 7$$

C. $$k > - 5$$

D. None of these.

View Answer

Releted Question 3

Let $$f\left( x \right) = \left| {x - 1} \right|.$$ Then

A. $$f\left( {{x^2}} \right) = {\left( {f\left( x \right)} \right)^2}$$

B. $$f\left( {x + y} \right) = f\left( x \right) + f\left( y \right)$$

C. $$f\left( {\left| x \right|} \right) = \left| {f\left( x \right)} \right|$$

D. None of these

View Answer

Releted Question 4

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

A. $$0 \leqslant x \leqslant 4$$

B. $$x \leqslant - 2\,{\text{or}}\,x \geqslant 4$$

C. $$x \leqslant 0\,{\text{or}}\,x \geqslant 4$$

D. None of these

View Answer

Let $$f\left( x \right) = nx + n - \left[ {nx + n} \right] + \tan \frac{{\pi x}}{2},$$ where $$\left[ x \right]$$ is the greatest integer $$ \leqslant x$$ and $$n\, \in \,N.$$ It is :

Releted MCQ Question on
Calculus >> Function

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

Let $$f\left( x \right) = \left| {x - 1} \right|.$$ Then

If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

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Let $$f\left( x \right) = nx + n - \left[ {nx + n} \right] + \tan \frac{{\pi x}}{2},$$ where $$\left[ x \right]$$ is the greatest integer $$ \leqslant x$$ and $$n\, \in \,N.$$ It is :

Releted MCQ Question on Calculus >> Function

Let $$R$$ be the set of real numbers. If $$f:R \to R$$ is a function defined by $$f\left( x \right) = {x^2},$$ then $$f$$ is:

The entire graphs of the equation $$y = {x^2} + kx - x + 9$$ is strictly above the $$x$$-axis if and only if

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If $$x$$ satisfies $$\left| {x - 1} \right| + \left| {x - 2} \right| + \left| {x - 3} \right| \geqslant 6,$$ then

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