Home
Class 11
MATHS
If f is a function satisfying f(x+y)=f(x...

If `f` is a function satisfying `f(x+y)=f(x)xxf(y)` for all `x ,y in N` such that `f(1)=3` and `sum_(x=1)^nf(x)=120 ,` find the value of `n` .

Text Solution

AI Generated Solution

To solve the problem, we need to find the value of \( n \) given the function \( f \) that satisfies the condition \( f(x+y) = f(x) \cdot f(y) \) for all \( x, y \in \mathbb{N} \), with \( f(1) = 3 \) and the summation \( \sum_{x=1}^{n} f(x) = 120 \). ### Step-by-Step Solution: 1. **Understanding the Functional Equation**: The equation \( f(x+y) = f(x) \cdot f(y) \) suggests that \( f \) is an exponential function. We can express \( f(n) \) in terms of \( f(1) \). 2. **Finding Values of \( f \)**: ...
Promotional Banner

Similar Questions

Explore conceptually related problems

If f is a function satisfying f(x+y)=f(x)f(y) for all x ,""""y in X such that f(1)=3 and sum_(x=1)^nf(x)=120 , find the value of n.

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . Then , sum_(k=1)^(n) f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)+f(y) for all x, y in R and f(1)=2 . Then sum_(k=1)^(n)f(k)=

Let f be a real valued function satisfying f(x+y)=f(x)f(y) for all x, y in R such that f(1)=2 . If sum_(k=1)^(n)f(a+k)=16(2^(n)-1) , then a=

Let f be a function satisfying f(x+y)=f(x) *f(y) for all x,y, in R. If f (1) =3 then sum_(r=1)^(n) f (r) is equal to

If f:RtoR satisfies f(x+y)=f(x)+f(y) for all x,y in R and f(1)=7, then sum_(r=1)^(n) f(r) , is

Let f be a real valued function, satisfying f (x+y) =f (x) f (y) for all a,y in R Such that, f (1_ =a. Then , f (x) =

If f:R to R satisfies f(x+y)=f(x)+f(y), for all x, y in R and f(1)=7, then sum_(r=1)^(n)f( r) is

If f:R rarr R satisfies f(x+y)=f(x)+f(y), for all x,y in R and f(1)=2 then sum_(r=1)^(7)f(1)