JEE Mains · Maths · STD 12 - 1. relation and function
Suppose that a function \(f: R \rightarrow R\) satisfies \(f(x+y)=f(x) f(y)\) for all \(x, y \in R\) and \(f(1)=3 .\) If \(\sum \limits_{i=1}^{n} f(i)=363,\) then \(n\) is equal to
- A \(6\)
- B \(5\)
- C \(7\)
- D \(4\)
Answer & Solution
Correct Answer
(B) \(5\)
Step-by-step Solution
Detailed explanation
\(f(x+y)=f(x) f(y)\) put \(x = y =1 \quad f(2)=(f(1))^{2}=3^{2}\) put \(x=2, y=1 \quad f(3)=(f(1))^{3}=3^{3}\) : Similarly \(f(x)=3^{x}\) \(\sum_{i=1}^{n} f(i)=363 \Rightarrow \sum_{i=1}^{n} 3^{i}=363\) \(\left(3+3^{2}+\ldots+3^{n}\right)=363\)…
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