Which inequality gives the domain of $y = \sqrt{2x - 3}$?
A - HSC - SSCE Mathematics Advanced - Question 3 - 2020 - Paper 1
Question 3
Which inequality gives the domain of $y = \sqrt{2x - 3}$?
A. $x \leq \frac{3}{2}$
B. $x \geq \frac{3}{2}$
C. $x < \frac{3}{2}$
D. $x > \frac{3}{2}$
Worked Solution & Example Answer:Which inequality gives the domain of $y = \sqrt{2x - 3}$?
A - HSC - SSCE Mathematics Advanced - Question 3 - 2020 - Paper 1
Step 1
Determine the domain restriction
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Answer
To find the domain of the function y=2x−3, we need to ensure that the expression inside the square root is non-negative. This leads us to the inequality:
2x−3≥0
Step 2
Solve the inequality
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Answer
Solving the inequality gives:
2x≥3⟹x≥23
Step 3
Choose the correct answer
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Answer
Based on the solution, the correct inequality representing the domain of the function is:
