What is the domain of $f(x) = \frac{1}{\sqrt{1 - x}}$?
A - HSC - SSCE Mathematics Advanced - Question 3 - 2023 - Paper 1
Question 3
What is the domain of $f(x) = \frac{1}{\sqrt{1 - x}}$?
A. $x < 1$
B. $x \leq 1$
C. $x > 1$
D. $x \geq 1$
Worked Solution & Example Answer:What is the domain of $f(x) = \frac{1}{\sqrt{1 - x}}$?
A - HSC - SSCE Mathematics Advanced - Question 3 - 2023 - Paper 1
Step 1
Step 1: Identify the constraints
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Answer
To find the domain of the function f(x)=1−x1, we need to ensure that the expression under the square root is non-negative and that the denominator is not zero. This means we have the following conditions:
1−x>0 (the square root must be defined)
1−x=0 (the denominator cannot be zero)
Step 2
Step 2: Solve the inequalities
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Answer
From the first condition 1−x>0, we can rearrange it to find:
x<1.
The second condition 1−x=0 implies:
x=1.
Thus, the only valid restriction for the domain is x<1.
Step 3
Step 3: Conclusion
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Answer
The domain of the function is therefore x<1, which corresponds to option A.
