फलन \(f:\mathbb{R}\to\mathbb{R}\) को (f(x)=\sqrt{ax-2+4}) से परिभाषित करना है। पूरे \(\mathbb{R}\) पर फलन बनने के लिए (a) की सही शर्त क्या है?
A function \(f:\mathbb{R}\to\mathbb{R}\) is to be defined by (f(x)=\sqrt{ax-2+4}). What is the correct condition on (a) for it to be a function on all of \(\mathbb{R}\)?
Explanation opens after your attempt
Correct Answer
A. \(\ a\ge0\)
Concept
The expression \(ax^2+4\) stays non-negative for all \(x\in\mathbb{R}\) only when \(a\ge0\). In square-root functions the radicand must be non-negative.
Why this answer is correct
The correct answer is A. \(\ a\ge0\). The expression \(ax^2+4\) stays non-negative for all \(x\in\mathbb{R}\) only when \(a\ge0\). In square-root functions the radicand must be non-negative.
Exam Tip
\(ax^2+4\) सभी \(x\in\mathbb{R}\) के लिए अऋण तभी रहता है जब \(a\ge0\) हो। मूल वाले फलन में भीतर की राशि अऋण चाहिए।
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