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If (f:\mathbb{R}\to[1,\infty)), (f(x)=x^2+1), which statement is correct?यदि (f:\mathbb{R}\to[1,\infty)), (f(x)=x^2+1), तो सही कथन कौन-सा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: It is ontoयह आच्छादक है
Step 1: (x^2\ge0), so (x^2+1\ge1). Step 2: For every (y\ge1), take (x=\sqrt{y-1}), then (f(x)=y). Step 3: The range of (x^2+a) is directly ([a,\infty)).चरण 1: (x^2\ge0), इसलिए (x^2+1\ge1)। चरण 2: हर (y\ge1) के लिए (x=\sqrt{y-1}) लेने पर (f(x)=y) मिलता है। चरण 3: (x^2+a) का परास सीधे ([a,\infty)) होता है।
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