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If (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{x^2-1}{x^2+1}), why is (f) not onto?यदि (f:\mathbb{R}\to[-1,1]), (f(x)=\frac{x^2-1}{x^2+1}) है, तो (f) आच्छादी क्यों नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Because (1) is not obtainedक्योंकि (1) नहीं मिलता
Step 1: (\frac{x^2-1}{x^2+1}=1-\frac{2}{x^2+1}). Step 2: This value is always less than (1), so (1) is never obtained. Step 3: For rational functions, checking endpoint values is very important.चरण 1: (\frac{x^2-1}{x^2+1}=1-\frac{2}{x^2+1}) है। चरण 2: यह मान (1) से हमेशा छोटा रहता है, इसलिए (1) कभी नहीं मिलता। चरण 3: भिन्नात्मक फलनों में सीमा के सिरों की जांच बहुत जरूरी है।
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