Let `f(x)=(1+1/x)^x and g(x)=(1+1/x)^(x+1),` both f and being defined for `x >0,` then prove that f(x) is increasing and g(x) is decreasing.

Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)) . Then,

Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)) . Then,

Let f(x)=(1)/(x) and g(x)=(1)/(sqrt(x)) . Then,

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

Let f(x)=(1)/(1+x^(2)) and g(x) is the inverse of f(x) ,then find g(x)

let ( f(x) = 1-|x| , |x| 1 ) g(x)=f(x+1)+f(x-1)

let f (x) = sin ^(-1) ((2g (x))/(1+g (x)^(2))), then which are correct ? (i) f (x) is decreasing if g (x) is increasig and |g (x) gt 1 (ii) f (x) is an increasing function if g (x) is increasing and |g (x) |le 1 (iii) f (x) is decreasing function if f(x) is decreasing and |g (x) | gt 1

let f (x) = sin ^(-1) ((2g (x))/(1+g (x)^(2))), then which are correct ? (i) f (x) is decreasing if g (x) is increasig and |g (x) gt 1 (ii) f (x) is an increasing function if g (x) is increasing and |g (x) |le 1 (iii) f (x) is decreasing function if f(x) is decreasing and |g (x) | gt 1

Let g(x)=f(x)+f(1-x) and f'(x)<00<=x<=1. Then