If for all `x,y` the function `f` is defined by `f(x)+f(y)+f(x).f(y)=1` and `f(x)gt0.` Then show `f'(x)=0`

The function f is defined by : f(x)= {(1-x,x 0):} . Draw the graph of f (x).

A function is defined as f(x) = {{:(e^(x)",",x le 0),(|x-1|",",x gt 0):} , then f(x) is

If f is a function satisfying f(x+y)= f(x) f(y) for all x,y in N such that f(1)=3 and sum_(x=1)^n f(x)=120 , find the value of n.

Let the function f satisfies f(x).f ′ (−x)=f(−x).f ′ (x) for all x and f(0)=3 The value of f(x).f(-x) for all x is

If the function f is defined by f(x)={(7" , "xne0),(a-1" , "x=0):} and f is continuous at x=0 then value of 'a' is _____

If the function f is defined by f(x) = {(3,,x,ne,0),(a+1,,x,=,0):} and f is continuous at x = 0, then value of a is :

If the function f is defined by f(x) = {(5,,x,ne,0),(a-1,,x,=,0):} and f is continuous at x = 0, then value of a is :

Let f be differentiable function satisfying f((x)/(y))=f(x) - f(y)"for all" x, y gt 0 . If f'(1) = 1, then f(x) is

The solution of (dy)/(dx)+yf'(x)-f(x).f'(x)=0,y!=f(x) is