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

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

Options:

  1. x >= 1
  2. x > 1
  3. x <= 1
  4. x < 1

Correct Answer: x >= 1

Solution: 

The expression under the square root must be non-negative, so x - 1 >= 0, hence x >= 1.

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

Practice Questions

Q1
What is the domain of the function f(x) = sqrt(x - 1)?
  1. x >= 1
  2. x > 1
  3. x <= 1
  4. x < 1

Questions & Step-by-Step Solutions

What is the domain of the function f(x) = sqrt(x - 1)?
  • Step 1: Identify the function, which is f(x) = sqrt(x - 1).
  • Step 2: Understand that the square root function is only defined for non-negative numbers.
  • Step 3: Set up the inequality for the expression under the square root: x - 1 >= 0.
  • Step 4: Solve the inequality by adding 1 to both sides: x >= 1.
  • Step 5: Conclude that the domain of the function is all x values that are greater than or equal to 1.
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