If `f(x+y)=af(x)+bf(y)` and f takes a value 0 only for 0, i.e, `f(0)=0`. Then find value of 2a+5b.

If f(x-y), f(x) f(y) and f(x+y) are in A.P. for all x, y in R and f(0)=0. Then,

If f(x-y), f(x) f(y), and f(x+y) are in A.P. for all x, y, and f(0) ne 0, then

Consider a real-valued function defined by the relation f(x+2y)=f(x)+mf(y)AAquad m!=0 for all values of x and y .If f'(0)=3 and f(2)= 4 then find the value of 4m .

Consider a real-valued function defined by the relation f(x+2y)=f(x)+mf(y)AAquad m!=0 for all values of x and y .If f'(0)=3 and f(2)= 4 then find the value of 4m .

Let f(x) is a differentiable function on x in R , such that f(x+y)=f(x)f(y) for all x, y in R where f(0) ne 0 . If f(5)=10, f'(0)=0 , then the value of f'(5) is equal to

If f (x) is continous on [0,2], differentiable in (0,2) f (0) =2, f(2)=8 and f '(x) le 3 for all x in (0,2), then find the value of f (1).

If (x+f(y))=f(x)+y AA x,y in R and f(0)=1 then find the value of f(7).

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

A function f:R rarr R" satisfies the equation f(x+y)=f(x)f(y) for all values of x" and "y and for any x in R,f(x)!=0 . Suppose the function is differentiable at x=0" and "f'(0)=2 , then for all x in R,f(x)=

If y=f(x)" and "ycosx+cosy=pi , then the value of f''(0) is