Question:
The domain of the function \(f(x) = \sqrt{7 - 11x}\) is
The domain of the function \(f(x) = \sqrt{7 - 11x}\) is
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Always check inequality direction when multiplying/dividing by negative.
Updated On: Apr 25, 2026
- \((- \infty , - 1]\)
- \(\left[\frac{7}{11}, \infty\right)\)
- \(\left(-\infty , \frac{7}{11}\right]\)
- \(\left[\frac{7}{11}, 1\right]\)
- \([-1, 1]\)
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Concept:
For square root, inside \(\geq 0\): \(7 - 11x \geq 0\).
Step 2: Detailed Explanation:
\(7 - 11x \geq 0 \implies -11x \geq -7 \implies x \leq \frac{7}{11}\).
Thus domain is \((-\infty, \frac{7}{11}]\).
Step 3: Final Answer:
Option (C).
For square root, inside \(\geq 0\): \(7 - 11x \geq 0\).
Step 2: Detailed Explanation:
\(7 - 11x \geq 0 \implies -11x \geq -7 \implies x \leq \frac{7}{11}\).
Thus domain is \((-\infty, \frac{7}{11}]\).
Step 3: Final Answer:
Option (C).
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