Let `f(x+y)-axy=f(x)+by^(2),AA x,y in R,f(1)=8,f(2)=32`, then `a+b=?`

If f:R rArr R such that f(x+y)-kxy=f(x)+2y^(2) for all x,y in R and f(1)=2,f(2)=8 then f(12)-f(6) is

If f:R rarr R be a differentiable function such that f(x+2y)=f(x)+f(2y)+4xy, AA x,y in R , f(2)=10 , then f(3)=?

Let f(x+y)+f(x-y)=2f(x)f(y)AA x,y in R and f(0)=k, then

Let f:R rarr R be a differential function satisfy f(x)=f(x-y)f(y)AA x,y in R and f'(0)=a,f'(2)=b then f'(-2)=

Let f:R rarr R^(*) be a derivable function such that f(x+y)=3f(x)f(y),AA x,y in R with f(1)=(2)/(3) ,then sum_(r=1)^(oo)(1)/(f(r)) is equal to

Let f(x) be a differentiable function satisfying f(y)f((x)/(y))=f(x)AA,x,y in R,y!=0 and f(1)!=0,f'(1)=3 then

If f((x+2y)/(3))=(f(x)+2f(y))/(3)AA x,y in R and f'(0)=1,f(0)=2 then find f(x) .

If f:R rarr R is continuous such that f(x+y)=f(x)*f(y)AA x,y in R and f(1)=2 then f(100)=

Let a function f:R rarr R be such that f(1)=2 , f'(0) = ln2 and f(x+y)=2^(x)f(y)+4^(y)f(x),AA x,y in R . If f'(2)=k ln2 ,then number of divisors of k ,is

Let f((x+y)/(2))=(f(x)+f(y))/(2),x,y in R, if f'(0)=-1, then f'((x)/(2))=