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Which of the following functions is continuous on the interval [0, 1]?

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Question: Which of the following functions is continuous on the interval [0, 1]?

Options:

  1. f(x) = 1/x
  2. f(x) = x^3
  3. f(x) = sqrt(x)
  4. f(x) = 1/(x-1)

Correct Answer: f(x) = x^3

Solution: 

f(x) = x^3 is a polynomial function and is continuous on the interval [0, 1].

Which of the following functions is continuous on the interval [0, 1]?

Practice Questions

Q1
Which of the following functions is continuous on the interval [0, 1]?
  1. f(x) = 1/x
  2. f(x) = x^3
  3. f(x) = sqrt(x)
  4. f(x) = 1/(x-1)

Questions & Step-by-Step Solutions

Which of the following functions is continuous on the interval [0, 1]?
  • Step 1: Identify the function given in the question, which is f(x) = x^3.
  • Step 2: Understand that polynomial functions, like f(x) = x^3, are continuous everywhere on the real number line.
  • Step 3: Recognize that the interval [0, 1] is part of the real number line.
  • Step 4: Conclude that since f(x) = x^3 is a polynomial function, it is continuous on the interval [0, 1].
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