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For which value of \(x\) is the function \(f(x)=\operatorname{sgn}(x+7)\) equal to zero?फलन \(f(x)=\operatorname{sgn}(x+7)\) किस \(x\)-मान पर शून्य होता है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: \(x=-7\)\(x=-7\)
The signum function \(\operatorname{sgn}(u)\) equals zero only when \(u=0\). Here, \(u=x+7\), so solving \(x+7=0\) gives \(x=-7\). Therefore, option A is correct. Exam tip: To find where \(\operatorname{sgn}(g(x))=0\), set the inner expression \(g(x)\) equal to zero.साइनम फलन \(\operatorname{sgn}(u)\) का मान शून्य तभी होता है जब \(u=0\) हो। यहाँ \(u=x+7\), इसलिए \(x+7=0\) रखने पर \(x=-7\) प्राप्त होता है। अतः सही उत्तर विकल्प A है। परीक्षा-युक्ति: \(\operatorname{sgn}(g(x))=0\) के लिए सीधे \(g(x)=0\) हल करें।
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