The equation `|x|+|x/(x-1)|=x^(2)/(|x-1|)` is always true for x belongs to A) {0} , B) `(1, infty)`, C) `(-1,1)`, D) `(-infty,infty)`

The equation |x|+|x/(x-1)|=x^(2)/(|x-1|) is always true for x belongs to A) {0}U (1,infty) , B) (1, infty) , C) (-1,1) , D) (-infty,infty)

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 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)

If x satisfies the inequations 2x-7 lt 11 and 3x+4 lt- 5 , then x lies in the interval a) (-infty,3) b) (-infty,2) c) (-infty,-3) d) (-infty,infty)

If log_(0.3) (x-1) lt log _(0.09) (x-1) , " then " x ne 1 lies in : a)(1,2) b)(0,1) c) (1,infty) d) (2,infty)

Let f (x) = x^3 -6 x^2 +9x +18, then f(x) is strictly decreasing in- A) (- infty ,1) B) (3, infty ) C) (- infty ,1]U[3, infty ) D) (1, 3)

The function f(x)= [x(x-2)]^2 is increasing in the set a) (-infty,0) cup (2,infty) b) (-infty,1) c) (0,1)cup(2,infty) d) ( 1 , 2 )

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)

The function f(x)=x^3-3x^2-24x+5 is an increasing function in the interval a) (-infty,-2) cup (4,infty) b) (-2,infty) c) (-2,4) d) (-infty,4)

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]