Let a function `f:R rarr R` such that `f(1)=2` and `f(x+y)=2^(x)f(y)+4^(y)f(x)AA x,y in R`. If `f'(2)=kln2` ,then the value of k is

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

If a function f:R rarr R be such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1AA x,y in R then f(2)=

Determine all functions f:R rarr R such that f(x-f(y))=f(f(y))+xf(y)+f(x)-1quad AA x,y>=0in R

Consider a differentiable function f:R rarr R for which f'(0)=ln2 and f(x+y)=2^(x)f(y)+4^(y)f(x)AA x,y in R which of the following is /are correct?

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The value of f(4) is

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

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The minimum value of f(x) is

Consider a differentiable f:R to R for which f(1)=2 and f(x+y)=2^(x)f(y)+4^(y)f(x) AA x , y in R. The number of solutions of f(x)=2 is

Let f:R to R such that f(x+y)+f(x-y)=2f(x)f(y) for all x,y in R . Then,