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Which of the following statements is true regarding the function f(x) = 1/(x-3)?

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Question: Which of the following statements is true regarding the function f(x) = 1/(x-3)?

Options:

  1. Continuous at x = 3
  2. Discontinuous at x = 3
  3. Continuous everywhere
  4. Discontinuous everywhere

Correct Answer: Discontinuous at x = 3

Solution: 

The function f(x) = 1/(x-3) is discontinuous at x = 3 because it is undefined at that point.

Which of the following statements is true regarding the function f(x) = 1/(x-3)?

Practice Questions

Q1
Which of the following statements is true regarding the function f(x) = 1/(x-3)?
  1. Continuous at x = 3
  2. Discontinuous at x = 3
  3. Continuous everywhere
  4. Discontinuous everywhere

Questions & Step-by-Step Solutions

Which of the following statements is true regarding the function f(x) = 1/(x-3)?
  • Step 1: Identify the function given, which is f(x) = 1/(x-3).
  • Step 2: Look for values of x that make the function undefined. This happens when the denominator is zero.
  • Step 3: Set the denominator (x - 3) equal to zero: x - 3 = 0.
  • Step 4: Solve for x: x = 3.
  • Step 5: Since the function is undefined at x = 3, it means there is a discontinuity at this point.
  • Step 6: Conclude that the function f(x) = 1/(x-3) is discontinuous at x = 3.
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