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If f(x) = x^3 - 3x + 2, then f(x) is continuous at:

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Question: If f(x) = x^3 - 3x + 2, then f(x) is continuous at:

Options:

  1. All x
  2. x = 0
  3. x = 1
  4. x = -1

Correct Answer: All x

Solution: 

f(x) is a polynomial function and is continuous for all x.

If f(x) = x^3 - 3x + 2, then f(x) is continuous at:

Practice Questions

Q1
If f(x) = x^3 - 3x + 2, then f(x) is continuous at:
  1. All x
  2. x = 0
  3. x = 1
  4. x = -1

Questions & Step-by-Step Solutions

If f(x) = x^3 - 3x + 2, then f(x) is continuous at:
  • Step 1: Identify the function 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 the real number line.
  • Step 4: Conclude that since f(x) is a polynomial, it is continuous for all values of x.
  • Continuity of Polynomial Functions – Polynomial functions are continuous for all real numbers.
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