Maths-
General
Easy

Question

Let f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where [ ] is the integral part of x. If the period of f(x) is pi, then a element of

  1. [4,6]
  2. [4,5)
  3. (4,3)
  4. (4,4)

hintHint:

In this question, we have to find the range of if f left parenthesis x right parenthesis equals cos space square root of p x where p equals left square bracket a right square bracket where [ ] is the integral part of x and the period of f(x) is pi. Firstly, we will find the period of the function given and equate it with the period given to get the value of p. Later, we can get the range of a.

The correct answer is: [4,5)


    f left parenthesis x right parenthesis equals cos space square root of p x
F u n d a m e n t a l space p e r i o d space o f space cos space x space i s space 2 straight pi.
So comma space fundamental space period space of space cos space square root of straight p straight x space is space fraction numerator 2 straight pi over denominator square root of straight p end fraction
As space period space of space straight f left parenthesis straight x right parenthesis space is space straight pi.
rightwards double arrow fraction numerator 2 straight pi over denominator square root of straight p end fraction equals straight pi
rightwards double arrow square root of straight p equals 2
rightwards double arrow straight p equals 4
rightwards double arrow 4 less or equal than straight p less than 5
rightwards double arrow straight a element of left square bracket 4 comma 5 right parenthesis

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