Let `y=f(x)` and `y = g(x)` be two monotonic, bijective functions such that `f(g(x)` is defined than `y=f(g(x))` is

If f:X to Y and g:Y to Z be two bijective functions, then prove that (gof)^(-1) =f^(-1)og(-1) .

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let f (xy) =g (x). G (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

Let y=f(x),y=g(x),y=h(x) be three invertible functions defined from R rarr R Then y=f(x)+g(x)+h(x) is

Let f(x) be a function such that f(x+y)=f(x)+f(y) and f(x)=sin x g(x)" fora ll "x,y in R . If g(x) is a continuous functions such that g(0)=k, then f'(x) is equal to

Let f(x) be a function such that f(x+y)=f(x)+f(y) and f(x)=sin x g(x)" fora ll "x,y in R . If g(x) is a continuous functions such that g(0)=k, then f'(x) is equal to

Let f and g be two real valued functions ,defined by f(x) =x ,g(x)=[x]. Then find the value of f+g

Let f(x) be a function such that f(x).f(y)=f(x+y) , f(0)=1 , f(1)=4 . If 2g(x)=f(x).(1-g(x))

Let f(x) and g(x) be functions which take integers as arguments.Let f(x+y)=f(x)+g(y)+8 for all intege x and y.Let f(x)=x for all negative integers x and let g(8)=17. Find f(0) .