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Which conclusion is correct for \(f:\mathbb{R}\to \mathbb{R}\), \(f(x)=x^2-x\)?फलन \(f:\mathbb{R}\to \mathbb{R}\), \(f(x)=x^2-x\) के लिए कौन सा निष्कर्ष सही है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: Not ontoआच्छादक नहीं है
Step 1: \(x^2-x=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\). Step 2: The minimum value is \(-\frac{1}{4}\), so smaller values are not obtained. Step 3: For quadratics, use the vertex form to find the range.चरण 1: \(x^2-x=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\)। चरण 2: न्यूनतम मान \(-\frac{1}{4}\) है इसलिए इससे छोटी संख्याएँ नहीं मिलतीं। चरण 3: द्विघात फलन में शीर्ष बिंदु से परास निकालना आसान होता है।
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