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If f(x) = 1/(x-1), what is the point of discontinuity?

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Question: If f(x) = 1/(x-1), what is the point of discontinuity?

Options:

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

Correct Answer: x = 1

Solution: 

The function is discontinuous at x = 1 because it leads to division by zero.

If f(x) = 1/(x-1), what is the point of discontinuity?

Practice Questions

Q1
If f(x) = 1/(x-1), what is the point of discontinuity?
  1. x = 0
  2. x = 1
  3. x = -1
  4. x = 2

Questions & Step-by-Step Solutions

If f(x) = 1/(x-1), what is the point of discontinuity?
  • Step 1: Identify the function given, which is f(x) = 1/(x-1).
  • Step 2: Look for values of x that make the denominator zero. In this case, the denominator is (x-1).
  • Step 3: Set the denominator equal to zero: x - 1 = 0.
  • Step 4: Solve for x: x = 1.
  • Step 5: Conclude that the function is discontinuous at x = 1 because division by zero is not allowed.
  • Discontinuity – A point where a function is not defined or does not behave well, often due to division by zero.
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