Let `f(x)=x^2-2x ,x in R ,a n dg(x)=f(f(x)-1)+f(5-f(x))dot` Show that `g(x)geq0AAx in Rdot`

Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

Let f(x) = x - [x] , x in R then f(1/2) is

Let g(x)gt0andf'(x)lt0,AAx in R, then show g(f(x+1))ltg(f(x-1)) f(g(x+1))ltf(g(x-1))

Let f(x)=x+f(x-1) for AAx in R . If f(0)=1,f i n d \ f(100) .

Let f and g be differentiable functions such that: xg(f(x))f\'(g(x))g\'(x)=f(g(x))g\'(f(x))f\'(x) AA x in R Also, f(x)gt0 and g(x)gt0 AA x in R int_0^xf(g(t))dt=1-e^(-2x)/2, AA x in R and g(f(0))=1, h(x)=g(f(x))/f(g(x)) AA x in R Now answer the question: f(g(0))+g(f(0))= (A) 1 (B) 2 (C) 3 (D) 4

Consider f: R^(+)->R such that f(3)=1 for a in R^+ a n d """"f(x)dotf(y)+ f(3/x)f(3/y)=2f(x y)AAx ,y in R^+dot Then find f(x)dot

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these

Let f(x)=|x-1|dot Then (a) f(x^2)=(f(x))^2 (b) f(x+y)=f(x)+f(y) (c) f(|x|)=|f(x)| (d) none of these

Let f:N->N be defined by f(x)=x^2+x+1,x in N . Then f(x) is

Let A=R-{3} and B=R-[1]dot Consider the function f: AvecB defined by f(x)=((x-2)/(x-3))dot Show that f is one-one and onto and hence find f^(-1)