Home
Class 12
MATHS
If f(x) satisfies the relation f(x+y)=f(...

If `f(x)` satisfies the relation `f(x+y)=f(x)+f(y)` for all `x , y in Ra n df(1)=5,t h e n` (a)`f(x)i sa nod dfu n c t ion` (b)`f(x)` is an even function (c)`sum_(n=1)^mf(r)=5^(m+1)C_2` (d) `sum_(n=1)^mf(r)=(5m(m+2))/3`

Promotional Banner

Similar Questions

Explore conceptually related problems

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(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

A continuous function f(x)onRvec satisfies the relation f(x)+f(2x+y)+5x y=f(3x-y)+2x^2+1forAA x ,y in RdotT h e n findf(x)dot

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then find the value of f(7)dot

If f(x) satisfies the relation f((5x-3y)/2)=(5f(x)-3f(y))/2AAx ,y in R , and f(0)=3a n df^(prime)(0)=2, then the period of "sin"(f(x)) is (a) 2pi (b) pi (c) 3pi (d) 4pi

If a function satisfies (x-y)f(x+y)-(x+y)f(x-y)=2(x^2 y-y^3) AA x, y in R and f(1)=2 , then

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

If f((x+2y)/3)=(f(x)+2f(y))/3AAx ,y in Ra n df^(prime)(0)=1,f(0)=2, then find f(x)dot

If f(x+y)=f(x)+f(y)-x y-1AAx , y in Ra n df(1)=1, then the number of solution of f(n)=n , n in N , is 0 (b) 1 (c) 2 (d) more than 2