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What is the domain of the function f(x) = 1/(x-3)?

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Question: What is the domain of the function f(x) = 1/(x-3)?

Options:

  1. x ≠ 3
  2. x > 3
  3. x < 3
  4. All real numbers

Correct Answer: x ≠ 3

Solution: 

The function is undefined at x = 3, so the domain is x ≠ 3.

What is the domain of the function f(x) = 1/(x-3)?

Practice Questions

Q1
What is the domain of the function f(x) = 1/(x-3)?
  1. x ≠ 3
  2. x > 3
  3. x < 3
  4. All real numbers

Questions & Step-by-Step Solutions

What is the domain of the function f(x) = 1/(x-3)?
Correct Answer: x ≠ 3
  • Step 1: Identify the function given, which is f(x) = 1/(x-3).
  • Step 2: Understand that the function is a fraction, and a fraction is undefined when the denominator is zero.
  • Step 3: Find the denominator of the function, which is (x - 3).
  • Step 4: Set the denominator equal to zero to find where the function is undefined: x - 3 = 0.
  • Step 5: Solve for x: x = 3.
  • Step 6: Conclude that the function is undefined at x = 3.
  • Step 7: State the domain of the function, which includes all real numbers except x = 3. This can be written as x ≠ 3.
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