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Which of the following functions is continuous at x = 2?

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Question: Which of the following functions is continuous at x = 2?

Options:

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

Correct Answer: f(x) = x^2 - 4

Solution: 

f(x) = x^2 - 4 is a polynomial function and is continuous everywhere, including at x = 2.

Which of the following functions is continuous at x = 2?

Practice Questions

Q1
Which of the following functions is continuous at x = 2?
  1. f(x) = 1/x
  2. f(x) = x^2 - 4
  3. f(x) = sin(1/x)
  4. f(x) =

Questions & Step-by-Step Solutions

Which of the following functions is continuous at x = 2?
  • Step 1: Identify the function given in the question, which is f(x) = x^2 - 4.
  • Step 2: Recognize that f(x) = x^2 - 4 is a polynomial function.
  • Step 3: Understand that polynomial functions are continuous everywhere on the real number line.
  • Step 4: Conclude that since f(x) is a polynomial, it is continuous at x = 2.
No concepts available.
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