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Is the function (f:\mathbb{R}\to(-\infty,3]), where (f(x)=3-x^2), onto?फलन (f:\mathbb{R}\to(-\infty,3]) जहाँ (f(x)=3-x^2), सर्वाच्छादक है या नहीं?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Yes because for every (y\le3), (x=\sqrt{3-y}) can be takenहाँ क्योंकि हर (y\le3) के लिए (x=\sqrt{3-y}) लिया जा सकता है
Step 1: The maximum value of (3-x^2) is (3). Step 2: If (y\le3), then (x=\sqrt{3-y}) is real and (f(x)=y). Step 3: A function is onto when its range equals its codomain.चरण 1: (3-x^2) का अधिकतम मान (3) है। चरण 2: यदि (y\le3), तो (x=\sqrt{3-y}) वास्तविक है और (f(x)=y) मिलता है। चरण 3: परास और सहप्रांत समान हों तो फलन सर्वाच्छादक होता है।
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