The exhaustive values of x for which `f(x) = tan^-1 x - x` is decreasing is (i) `(1,infty)` (ii) `(-1,infty)` (iii) `(-infty,infty)` (iv) `(0,infty)`

The function f(x)=1/(1+x^2) is decreasing in the interval (i) (-infty,-1) (ii) (-infty,0) (iii) (1,infty) (iv) (0,infty)

Consider the equation log_2 ^2 x- 4 log_2 x- m^2 -2m-13=0,m in R. Let the real roots of the equation be x_1,x_2, such that x_1 < x_2 .The set of all values of m for which the equation has real roots is (i) (-infty ,0) (ii) (0,infty) (iii) [1, infty) (iv) (-infty,infty)

The domain of f(x)=log_x 12 is (i) (0,infty) (ii ) (0,1)cup (1,infty) (iii) (-infty,0) (iv) (2,12)

The value of x for which the function given by f(x)=2x^3-3x^2-12x+12 is increasing lies in: a) (-infty,-1)cup(2,infty) b) (-infty,-4)cup(2,infty) c) (-infty,0)cup(2,infty) d) (-infty,-2)cup(2,infty)

The complete set of values of a for which the function f(x)=tan^(-1)(x^(2)-18x +a)gt 0 AA x in R is a. (81, infty) b. [81,infty) c. (-infty,81) d. (-infty,81]

The function f(x) = x^2 is increasing in the interval: a)(-1,1) b) (-infty,infty) c) (0,infty) d) (-infty,0)

Let f^(prime)(x)>0 AA x in R and g(x)=f(2-x)+f(4+x). Then g(x) is increasing in (i) (-infty,-1) (ii) (-infty,0) (iii) (-1,infty) (iv) none of these

The function f(x)= x^2+2x+5 is strictly increasing in the interval: a) (-1,infty) b) (-infty,-1) c) [-1,infty) d) (-infty,-1]

The function f(x) = x^(3) - 6x^(2) +9x + 3 is decreasing for: a) (-infty,-1)cup(3,infty) b) (1,3) c) (3,infty) d) (1,4)