Multiple Choice Question (MCQ)

Which of the following is right to describe the function f(x) = \cos (x+\dfrac{\pi}{3} ), x\in R

  1. ×

    f(x) is an odd function

  2. ×

    f(x) is an even function

  3. ✓

    f(x) is a neither even nor odd function

  4. ×

    f(x) is a not only odd but also even function

Collected in the board: Trigonometry

Steven Zheng posted 2 years ago

Answer

  1. For an odd function, f(-x)=f(x)

    However, \cos(-x+\dfrac{\pi}{3})\ne-\cos(x+\dfrac{\pi}{3})

    Similarly, \cos(-x+\dfrac{\pi}{3})\ne\cos(x+\dfrac{\pi}{3})

    Therefore, f(x) is a neither even nor odd function. C is the choice.

Steven Zheng posted 2 years ago

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