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What is the domain of the function f(x) = 1/(x-3)?
What is the domain of the function f(x) = 1/(x-3)?
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Practice Questions
1 question
Q1
What is the domain of the function f(x) = 1/(x-3)?
x ≠ 3
x > 3
x < 3
All real numbers
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The function is undefined at x = 3, so the domain is x ≠ 3.
Questions & Step-by-step Solutions
1 item
Q
Q: What is the domain of the function f(x) = 1/(x-3)?
Solution:
The function is undefined at x = 3, so the domain is x ≠ 3.
Steps: 7
Show Steps
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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