The domain of `f(x)=1/(sqrt((x-2)(7-x))` is (i )`(2,infty)` (ii) `(7,infty)` (iii) `(2,7)` (iv) `(-infty,2)`

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 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)

If f(x)=sqrt((x-sinx)/(x+cos^2x)) , then lim_(x rarr infty)f(x) is

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

If the point (1, a) lies in between the lines x + y =1 and 2(x+y) = 3 then a lies in (i) (-infty,0)cup (1,infty) (ii) (0,1/2) (iii) (-infty,0)cup (1/2,infty) (iv) none of these

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)

If domain of f(x)=(sqrt(x^2-25)/(4-x^2)+ln(x^2+2x-15) "is" (-infty,alpha)cup(beta,infty) then value of (alpha^2+beta^2) is

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