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Which of the following real-valued functions has natural domain \\([-1,1]\\) and range \\([0,1]\\)?निम्नलिखित वास्तविक-मान फलनों में किसका प्राकृत डोमेन \\([-1,1]\\) तथा रेंज \\([0,1]\\) है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \\(\sqrt{1-x^2}\\)\\(\sqrt{1-x^2}\\)
For \\(\sqrt{1-x^2}\\), the radicand must satisfy \\(1-x^2\ge0\\), giving \\(-1\le x\le1\\). A square root is non-negative, and its maximum is 1 at \\(x=0\\). Thus the range is \\([0,1]\\). Exam tip: first impose the radicand condition.\\(\sqrt{1-x^2}\\) के लिए \\(1-x^2\ge0\\), इसलिए \\(-1\le x\le1\\)। वर्गमूल सदैव अऋणात्मक है और अधिकतम मान \\(x=0\\) पर 1 है। अतः रेंज \\([0,1]\\) है। परीक्षा टिप: वर्गमूल के भीतर का व्यंजक पहले अऋणात्मक लें।
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