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

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

Let f(x+1/y) +f(x-1/y) =2f(x) f(1/y) AA x, y in R , y!=0 and f(0)=0 then the value of f(1) +f(2)=

If f(x+f(y))=f(x)+yAAx ,y in Ra n df(0)=1, then prove that int_0^2f(2-x)dx=2int_0^1f(x)dxdot

If f (x/y)= f(x)/f(y) , AA y, f (y)!=0 and f' (1) = 2 , find f(x) .

Let f(x)=(x-1)(x-2)(x-3)(x-n),n in N ,a n df(n)=5040. Then the value of n is________

If f(x+y+1)={sqrt(f(x))+sqrt(f(y))}^2 and f(0)=1AAx ,y in R ,determine f(n),n in Ndot

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

If f(x+1)+f(x-1)=2f(x)a n df(0),=0, then f(n),n in N , is nf(1) (b) {f(1)}^n (c) 0 (d) none of these

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