Strictly increasing functions and strictly decreasing functions

Prove that the function f given by f(x)=log(cos x) is strictly increasing on (-(pi)/(2),0) and strictly decreasing on (0,(pi)/(2))

Prove that the function f given by f(x)=log cos x is strictly increasing on (-pi/2,0) and strictly decreasing on (0,pi/2)

Prove that the function f given by f(x)=log sin,xf(x)=log sinquad x is strictly increasing on (0,(pi)/(2)) and strictly decreasing on ((pi)/(2),pi)

A function f is said to be increasing/strictly increasing/decreasing/strictly decreasing at x_0, if there exists an interval I containing x_0, such that f is increasing /strictly increasing /decreasing /strictly decreasing, respectively, in I. Which of the following statements regarding the above definition is FALSE?

Show that the function f(x) = x^(2) is (a) strictly increasing on [0, oo] (b) strictly decreasing on [-oo, 0] (c) neither strictly increasing nor strictly decreasing on R

show that the function f(x)=sin x is strictly increasing in (0,(pi)/(2)) strictly decreasing in ((pi)/(2),pi)

Without using the derivative,show that the function f(x)=|x| is strictly increasing in (0,oo) strictly decreasing in (-oo,0)

The function f(x)=(x)/(1+|x|) is (a) strictly increasing (b) strictly decreasing (c) neither increasing nor decreasing (d) none of these

Without using the derivative,show that the function f(x)=|x| is (a) strictly increasing in (0,oo)( b) strictly decreasing in (-oo,0)

Show that the function given by f (x) = sinx is (a) strictly increasing in (0,pi/2) (b) strictly decreasing in (pi/2,pi) (c) neither increasing nor decreasing in (0, pi)