[f(x)=cos^(-1)x" is decreasing in "],[qquad (-1,0)],[bigcirc(0,pi/2)],[bigcirc(-1,1)],[" O None "]

Let f(x)=cos^(-1)((x^2)/(1+x^2)) . The range of f is a) [0,pi/2] b) [-pi/2,pi/2] c) [-pi/2,0] d)None of these

On which of the following intervals is the function f given by f(x)=x^(100)+sinx-1 strictly decreasing ? (A) (0, 1) (B) (pi/2,pi) (C) (0,pi/2) (D) None of these

If the function f(x)=2cot x+(2a+1)ln|cos ecx|+(2-a)x is strictly decreasing in (0,(pi)/(2)) then range of a is

Show that the function f(x)=cot^(-1)(sin x+cos x) is decreasing on (0,pi/4) and increasing on (pi/4,pi/2)

Statement 1: Let f(x)=sin(cos x) in [0,(pi)/(2)]* Then f(x) is decreasing in [0,(pi)/(2)] Statement 2:cos x is a decreasing function AA x in[0,(pi)/(2)]

On which of the following intervals is the function x^(100)+sin x-1 decreasing? (a) (0,(pi)/(2))(b)(0,1)(c)((pi)/(2),pi)( d) none of these

Let f''(x)gt0 and phi(x)=f(x)+f(2-x),x in(0,2) be a function then the function phi(x) is (A) increasing in (0,1) and decreasing (1,2) (B) decreasing in (0, 1) and increasing (1,2) (C) increasing in (0, 2) (D) decreasing in (0,2)

Range of the function f(x)=(cos^(-1)abs(1-x^(2))) is a. [0,pi/2] " " b. [0,pi/3] c. (o,pi) " " d. (pi/2,pi)

Statement 1: Let f(x)=sin(cos x) \ i n \ [0,pi/2] . Then f(x) is decreasing in [0,pi/2] Statement 2: cosx is a decreasing function AAx in [0,pi/2]