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If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?

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Question: If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?

Options:

  1. Continuous
  2. Not Continuous
  3. Only left continuous
  4. Only right continuous

Correct Answer: Continuous

Solution: 

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

If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?

Practice Questions

Q1
If f(x) = x^2 - 4, what is the continuity of f(x) at x = 2?
  1. Continuous
  2. Not Continuous
  3. Only left continuous
  4. Only right continuous

Questions & Step-by-Step Solutions

If f(x) = x^2 - 4, what is the continuity of f(x) 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) is a polynomial function because it is made up of x raised to a power and constants.
  • Step 3: Understand that polynomial functions are continuous everywhere on the real number line.
  • Step 4: Since f(x) is continuous everywhere, it is also continuous at x = 2.
  • Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.
  • Evaluating Functions – Evaluating the function at a specific point to determine continuity.
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