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For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.

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Question: For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.

Options:

  1. None
  2. x = 1
  3. x = -1
  4. x = 2

Correct Answer: None

Solution: 

f(x) is a polynomial function and is continuous everywhere, hence no points of discontinuity.

For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.

Practice Questions

Q1
For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.
  1. None
  2. x = 1
  3. x = -1
  4. x = 2

Questions & Step-by-Step Solutions

For the function f(x) = x^3 - 3x + 2, find the points of discontinuity.
  • Step 1: Identify the function given, which is f(x) = x^3 - 3x + 2.
  • Step 2: Recognize that this function is a polynomial function.
  • Step 3: Understand that polynomial functions are continuous everywhere on their domain.
  • Step 4: Conclude that since f(x) is a polynomial, there are no points of discontinuity.
  • Continuity of Polynomial Functions – Polynomial functions are continuous everywhere on their domain, which is all real numbers.
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