किस विकल्प में \(f:\mathbb{R}\to\mathbb{R}\) पूरे \(\mathbb{R}\) पर वैध फलन नहीं है?
Which option is not a valid function \(f:\mathbb{R}\to\mathbb{R}\) on all of \(\mathbb{R}\)?
Explanation opens after your attempt
Correct Answer
D. (f(x)=\sqrt{2x-1})
Concept
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.
Why this answer is correct
The correct answer is D. (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.
Exam Tip
\(\sqrt{2x-1}\) 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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