Show that `y = log(1+x) - 2x/(2+x), x>-1`, is an increasing function of x. throughout its domain.

Show that y = log (1 + x) - (2x)/(2 + x) is strictly increasing funtion of x for all values of x gt - 1 .

If x> - 1 , show that x/(sqrt(1+x)) -log(1+x) + 9 is an increasing function of x.

Show that the function f (x) = (x)/(1+|x|) is a strict increasing function.

Show that the function f(x) = x -(1)/(x) is a strict increasing function fox x > 0

Show that f(x) = 2x+Cot^-1 x +log(sqrt(1+x^2)-x) is increasing in R.

Show that the function f(x)=x^(7)+8x^(5)+1 is increasing function for all values of x.

Let f: RvecR be differentiable and strictly increasing function throughout its domain. Statement 1: If |f(x)| is also strictly increasing function, then f(x)=0 has no real roots. Statement 2: When xvecooorvec-oo,f(x)vec0 , but cannot be equal to zero.

Show that the function x+1/x, x ge 1 is increasing.

f(x)=log(x-[x]) , where [*] denotes the greatest integer function. find the domain of f(x).