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If (f:[1,\infty)\to\mathbb{R}), (f(x)=\sqrt{x-1}), why is it not onto?यदि (f:[1,\infty)\to\mathbb{R}), (f(x)=\sqrt{x-1}) है, तो यह आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because negative values are not obtainedक्योंकि ऋणात्मक मान नहीं मिलते
Step 1: A square-root value is always (0) or positive. Step 2: The codomain (\mathbb{R}) contains negative values such as (-1), which are not obtained. Step 3: A square-root function is not onto a full real codomain.चरण 1: वर्गमूल का मान हमेशा (0) या धनात्मक होता है। चरण 2: सहप्रांत (\mathbb{R}) में (-1) जैसे ऋणात्मक मान हैं, जो नहीं मिलते। चरण 3: वर्गमूल फलन को वास्तविक सहप्रांत देने पर आच्छादीपन नहीं रहता।
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