The domain of `f(x)=sqrt(log((7x-x^2)/12))` is (i) `(-infty,infty)` (ii) `(-infty,4]` (iii)` [3,infty)` (iv) [3,4]

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

Find the range of f(x)= (x^2 + x +2)/(x^2 + x +1) (-infty lt x lt 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)

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 range of the function f(x)=(x^2-x+1)/(x^2+x+1) where x , in R is a) (-infty, 3] b) (-infty, infty) c) [3, infty) d) [1/3,3]

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 domain of the function f(x)=sin x, is (-infty, infty) . The range of f(x) is

Find the domain of the following y = tan^(-1) ( sqrt (x^(2) - 1)) a. (-infty,-2]cup[1, infty) b. (-infty,-1] c. (-infty,-1]cup[2, infty) d. (-infty,-1]cup[1, infty)

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)

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)