Home
Class 12
MATHS
If f(x+y)=f(x)f(y) and sum(x=1)^(oo)f(x)...

If `f(x+y)=f(x)f(y) and sum_(x=1)^(oo)f(x)=2,x,y in N`, where N is the set of all natural numbers , then the value of `(f(4))/(f(2))` is :

A

`2/3`

B

`1/9`

C

`1/3`

D

`4/9 `

Text Solution

AI Generated Solution

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • JEE MAINS

    JEE MAINS PREVIOUS YEAR|Exercise Physics|30 Videos

  • JEE MAINS 2021

    JEE MAINS PREVIOUS YEAR|Exercise Mathematics (Section A )|20 Videos

Similar Questions

Explore conceptually related problems

If f(x+y)=f(x)*f(y) and f(1)=4. Find sum_(r=1)^(n)f(r)

If f(x)+f(y)+f(xy)=2+f(x)f(y) for all x, y in R and f(x) is a polynomial function with f(4)=65 then find the value of (f(5))/(7) is (where f(1) ne 1) .

Knowledge Check

  • 'If f(x+ y) = f (x)+ f (y) AA x,y R and f (1) = lamda , then f(n), n in N is

    A
    `lamda^n`
    B
    ` (1)/(lamda^n)`
    C
    `n lamda`
    D
    None

  • If f(x+y)=2f(x) f(y) for all x,y where f'(0)=3 and f(4)=2, then f'(4) is equal to

    A
    6
    B
    12
    C
    4
    D
    none of these

  • Let f[x + y)=f{x)+f (y) and f(x) = x^2 g(x) for all x, y in R , where g{x) is continuous function. Then f'(x) is equal to

    A
    g'(x)
    B
    g(0)
    C
    g(0) + g'(0)
    D
    0

    • Similar Questions

    Explore conceptually related problems

    If 2f(x+y)=f(x).f(y) for all real x, y. where f'(0)=3 and f(4)=25 , then the value of f'(4) is equal to

    If f(x)=(a^(x)+a^(-x))/(2) and f(x+y)+f(x-y)=kf(x)f(y) then k=

    The natural number a for which sum_(k=1)^(n)f(a+k)=16(2^(n)-1) where the function f satisfies the relation f(x+y)=f(x)*f(y) for all natural numbers x,y and further f(1)=2 is

    If f (x) is a function satisfying f (x + y) = f (x) f (y) AA x, y in N, such that f (1) = 3 and sum_(x=1) ^(n) f (x) = 120, then the value of n is

    If f(2(x)/(y))=f(2x)-f(y) for all x,y>0 and f(3)=2, then the value of [f(7)], is

    Home
    Profile