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JEE Main20211 Sep 2021Evening ShiftMathematicsFunctionsActual

The range of the function f ( x ) = log 5 3 + cos 3 π 4 + x + cos π 4 + x + cos π 4 - x - cos 3 π 4 - x is :

Options

  1. A1 5 ,   5
  2. B[ 0 ,   2 ]
  3. C( 0 ,   5 )
  4. D[ - 2 ,   2 ]

Correct answer

B. [ 0 ,   2 ]

Step-by-step solution

f ( x ) = log 5 ( 3 - 2 sin x + 2 cos x ) - 2 ≤ ( - 2 sin x + 2 cos x ) ≤ 2 ⇒ 1 ≤ ( 3 - 2 sin x + 2 cos x ) ≤ 5 ⇒ log 5 1 ≤ f ( x ) ≤ log 5 5 ⇒ 0 ≤ f ( x ) ≤ 2

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