\(R=\{(x,y)\in\mathbb{R}\times\mathbb{R}:x=y^3\}\) को \(\mathbb{R}\) से \(\mathbb{R}\) में संबंध माना जाए, तो यह फलन है या नहीं?
If \(R=\{(x,y)\in\mathbb{R}\times\mathbb{R}:x=y^3\}\) is considered as a relation from \(\mathbb{R}\) to \(\mathbb{R}\), is it a function?
Explanation opens after your attempt
A. हाँ, क्योंकि हर (x) के लिए \(y=\sqrt[3]{x}\) अद्वितीय हैYes, because for every (x), \(y=\sqrt[3]{x}\) is unique
Concept
Every real (x) has a unique real cube root. Hence this relation is a function from \(\mathbb{R}\) to \(\mathbb{R}\).
Why this answer is correct
The correct answer is A. हाँ, क्योंकि हर (x) के लिए \(y=\sqrt[3]{x}\) अद्वितीय है / Yes, because for every (x), \(y=\sqrt[3]{x}\) is unique. Every real (x) has a unique real cube root. Hence this relation is a function from \(\mathbb{R}\) to \(\mathbb{R}\).
Exam Tip
हर वास्तविक (x) का वास्तविक घनमूल अद्वितीय होता है। इसलिए यह संबंध \(\mathbb{R}\) से \(\mathbb{R}\) में फलन है।
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