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Which of the following functions is periodic?

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Question: Which of the following functions is periodic?

Options:

  1. f(x) = x
  2. f(x) = cos(x)
  3. f(x) = e^x
  4. f(x) = ln(x)

Correct Answer: f(x) = cos(x)

Solution: 

The cosine function is periodic with a period of 2π.

Which of the following functions is periodic?

Practice Questions

Q1
Which of the following functions is periodic?
  1. f(x) = x
  2. f(x) = cos(x)
  3. f(x) = e^x
  4. f(x) = ln(x)

Questions & Step-by-Step Solutions

Which of the following functions is periodic?
  • Step 1: Understand what a periodic function is. A periodic function is one that repeats its values at regular intervals.
  • Step 2: Identify the cosine function, which is written as cos(x).
  • Step 3: Determine the period of the cosine function. The period is the length of one complete cycle of the function.
  • Step 4: Recognize that the cosine function completes one full cycle when the input (x) increases by 2π.
  • Step 5: Conclude that since the cosine function repeats its values every 2π, it is a periodic function.
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