Let a function f be such that `f((1)/(r ))-5f(r)=3r,` for every `r ne 0`. Find `f(3)`.

Let f:R rarr R be a function such that f((x+y)/(3))=(f(x)+f(y))/(3),f(0)=0 and f'(0)=3

Let f:R rarr R be a function such that f(x)=x^(3)+x^(2)f'(1)+xf''(2)+f''(3) for x in R What is f(1) equal to

Let f_(1):R rarr R and f_(2):C rarr C are two functions such that f_(1)(x)=x^(3) and f_(2)=x^(3) .Prove that f_(1) and f_(2) are not same.

Let f:R rarr R-{3} be a function such that for some p>0,f(x+p)=(f(x)-5)/(f(x)-3) for all x in R. Then,period of f is

Let f:R rarr R be a twice differentiable function such that f(x+pi)=f(x) and f'(x)+f(x)>=0 for all x in R. show that f(x)>=0 for all x in R .

Let f : R to R be a function such that f(x+y) = f(x)+f(y),Aax, y in R. If f (x) is differentiable at x = 0, then

Let f:R to R be continuous function such that f(x)=f(2x) for all x in R . If f(t)=3, then the value of int_(-1)^(1) f(f(x))dx , is

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

Let f:R to R and g:R to R be differentiable functions such that f(x)=x^(3)+3x+2, g(f(x))=x"for all "x in R , Then, g'(2)=