JEE Mains · Maths · STD 12 - 1. relation and function
Let f and g be functions satisfying \( f(x+y)=f(x)f(y), f(1)=7 \) and \( g(x+y)=g(xy), g(1)=1 \) for all \( x, y\in\mathbb{N} \). If \( \sum_{x=1}^{n}(\frac{f(x)}{g(x)})=19607, \) then n is equal to:
- A 7
- B 5
- C 6
- D 4
Answer & Solution
Correct Answer
(B) 5
Step-by-step Solution
Detailed explanation
\(f(x+y)=f(x) \cdot f(y) \Rightarrow f(x)=a^x\) \(\left(\because f(1)=7 \Rightarrow=a^1=7\right)\) So \(f(x)=7^x\) Now \(g(x+y)=g(x y) \quad(\text { put } y=1)\) \(\Rightarrow g ( x +1)= g ( x )\) so \(g (1)= g (2)= g (3)=\ldots= g ( n )=1\) Given…
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