यदि \(f:\mathbb{Z}\to\mathbb{Z}\) को (f(n)=\frac{n-3-n}{3}) से दिया गया है, तो कौन सा कथन सही है?
If \(f:\mathbb{Z}\to\mathbb{Z}\) is given by (f(n)=\frac{n-3-n}{3}), which statement is correct?
Explanation opens after your attempt
B. यह फलन है क्योंकि \(n^3-n\) हमेशा (3) से विभाज्य होता हैIt is a function because \(n^3-n\) is always divisible by (3)
Concept
Since (n-3-n=n(n-1)(n+1)) is the product of three consecutive integers, it is divisible by (3). For codomain checking, focus on integrality.
Why this answer is correct
The correct answer is B. यह फलन है क्योंकि \(n^3-n\) हमेशा (3) से विभाज्य होता है / It is a function because \(n^3-n\) is always divisible by (3). Since (n-3-n=n(n-1)(n+1)) is the product of three consecutive integers, it is divisible by (3). For codomain checking, focus on integrality.
Exam Tip
(n-3-n=n(n-1)(n+1)) लगातार तीन पूर्णांकों का गुणनफल है, इसलिए (3) से विभाज्य है। सहप्रांत जांचने के लिए पूर्णांकता पर ध्यान दें।
Login to save your score, XP, coins and progress.