Show that `f(x) = (1)/((1 + x^(2)))` is increasing for all `x le 0`

Show that f(x) = (x - (1)/(x)) is increasing for all x in R, x ne 0 .

Show that f(x) = ((x -2))/((x +1)) is increasing for all x in R , except at x = -1

Show that f(x) = (x - (1)/(x)) is increasing for all x in R , where x != 0

Show that f(x)=(x-1)e^x+1 is an increasing function for all x > 0.

Show that f(x)=(x-1)e^(x)+1 is an increasing function for all x>0

Show that f(x)=(x-1)e^(x)+1 is an increasing function for all x>0

Show that f(x)=(x-1)e^x+1 is an increasing function for all x >0 .

Show that f(x)=x^(2)e^(-x), 0 le x le 2 is increasing in the indicated interval.

Show that f(x)={{:(x^(2),if, 0 le x le 1),(x ,if, 1 le x le 2):} is continuous on [0,2]

If f(x) = {{:(|1-4x^(2)|",",0 le x lt 1),([x^(2)-2x]",",1 le x lt 2):} , where [] denotes the greatest integer function, then A. f(x) is continuous for all x in [0, 2) B. f(x) is differentiable for all x in [0, 2) - {1} C. f(X) is differentiable for all x in [0, 2)-{(1)/(2),1} D. None of these