Question

The function f(x) = cosx+{x}
(where {.} denotes the fractional part function) is

(a) periodic with period 1
(b) periodic with peried π
(c) periodic with period 2π
(d) Not periodic​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The function f(x) = cosx + {x}

(where {.} denotes the fractional part function) is

(a) periodic with period 1

(b) periodic with peried π

(c) periodic with period 2π

(d) Not periodic

EVALUATION

Here the given function is

f(x) = cosx + {x}

Now

$\sf{ \cos(2\pi + x) = \cos x}$

So cos x is a periodic function of period 2π

Again

{ x + 1 } = {x}

So {x} is a periodic function of period 1

Since f(x) = cosx + {x}

So period of f(x)

= LCM { 2π , 1 }

Since 2π is irrational and 1 is rational

So the LCM does not exists

Hence f(x) is not a periodic function

FINAL ANSWER

Hence the correct option is (d) Not periodic

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