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Which option is not a valid function (f:\mathbb{R}\to\mathbb{R}) on all of (\mathbb{R})?किस विकल्प में (f:\mathbb{R}\to\mathbb{R}) पूरे (\mathbb{R}) पर वैध फलन नहीं है?
Answer and explanationउत्तर और व्याख्या
Correct answer:सही उत्तर: (f(x)=\sqrt{2x-1})(f(x)=\sqrt{2x-1})
The expression (\sqrt{2x-1}) is real only when (x\ge\frac{1}{2}). A function on all of (\mathbb{R}) needs a value for every real input.(\sqrt{2x-1}) वास्तविक तभी है जब (x\ge\frac{1}{2}) हो। पूरे (\mathbb{R}) पर फलन के लिए हर वास्तविक इनपुट पर मान चाहिए।
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