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If \(f:\mathbb{R}\to \left[-\frac{1}{4},\infty\right)\), \(f(x)=x^2-x\), what type is \(f\)?यदि \(f:\mathbb{R}\to \left[-\frac{1}{4},\infty\right)\), \(f(x)=x^2-x\), तो \(f\) कैसा है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Ontoआच्छादक है
Step 1: \(f(x)=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\). Step 2: Its range is \(\left[-\frac{1}{4},\infty\right)\), exactly the given codomain. Step 3: Once range and codomain match, onto is proved.चरण 1: \(f(x)=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\) है। चरण 2: इसका परास \(\left[-\frac{1}{4},\infty\right)\) है और यही सहक्षेत्र दिया गया है। चरण 3: परास और सहक्षेत्र बराबर मिलते ही आच्छादकता सिद्ध हो जाती है।
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