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If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?

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Question: If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?

Options:

  1. 0, Continuous
  2. 0, Not Continuous
  3. 1, Continuous
  4. 1, Not Continuous

Correct Answer: 0, Continuous

Solution: 

f(1) = 1^3 - 3(1) + 2 = 0. Since f(x) is a polynomial, it is continuous everywhere.

If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?

Practice Questions

Q1
If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?
  1. 0, Continuous
  2. 0, Not Continuous
  3. 1, Continuous
  4. 1, Not Continuous

Questions & Step-by-Step Solutions

If f(x) = x^3 - 3x + 2, what is the value of f(1) and is it continuous?
  • Step 1: Identify the function f(x) = x^3 - 3x + 2.
  • Step 2: Substitute x = 1 into the function to find f(1).
  • Step 3: Calculate f(1) by performing the operations: 1^3 - 3(1) + 2.
  • Step 4: Simplify the calculation: 1 - 3 + 2.
  • Step 5: Combine the numbers: 1 - 3 = -2, then -2 + 2 = 0.
  • Step 6: Conclude that f(1) = 0.
  • Step 7: Determine if the function is continuous. Since f(x) is a polynomial, it is continuous everywhere.
  • Function Evaluation – The process of substituting a specific value into a function to find its output.
  • Continuity of Functions – Understanding that polynomial functions are continuous everywhere on their domain.
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