JEE Mains · Maths · STD 12 - 1. relation and function
The number of functions \(f :\{1,2,3,4\} \rightarrow\{ a \in Z :| a | \leq 8\}\) satisfying \(f ( n )+\) \(\frac{1}{ n } f ( n +1)=1, \forall n \in\{1,2,3\}\) is
- A \(3\)
- B \(4\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(D) \(2\)
Step-by-step Solution
Detailed explanation
\(f:\{1,2,3,4\} \rightarrow\{ a \in Z :| a | \leq 8\}\) \(f( n )+\frac{1}{ n } f ( n +1)=1, \forall n \in\{1,2,3\}\) \(f( n +1)\) must be divisible by \(n\) \(f(4) \Rightarrow-6,-3,0,3,6\) \(f(3) \Rightarrow-8,-6,-4,-2,0,2,4,6,8\)…
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