" Let "g'(x)>0" and "f'(x)<0AA x in R." Then : "

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let g'(x)gt 0 and f'(x) lt 0 AA x in R , then

Let g(x) =1+x-[x] and f(x) ={{:(-1, if, x lt 0),(0, if, x=0),(1, if, x gt 0):} , then (f(g(2009)))/(g(f(2009)) =

Let g(x)=1+x-[x] and f(x)=-1 if x 0, then f|g(x)]=1x>0

Let f(x)>0 and g(x)>0 with f(x)>g(x)AA x in R are differentiable functions satisfying the conditions (i) f(0)=2,g(0)=1 , (ii) f'(x)=g(x) , (iii) g'(x)=f(x) then

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 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 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 and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

Suppose that f(0)=0 and f'(0)=2, and let g(x)=f(-x+f(f(x))). The value of g'(0) is equal to -