Find the set of all possible real value of a such that the inequality `(x-(a-1))(x-(a^2+2))<0` holds for all `x in (-1,3)dot`

Find the possible values of 'a' such that the inequality 3-x^(2)gt |x-a| has atleast one negative solution

Find all values of x that satisfies the inequality (2x-3)/((x-2)(x-4)) lt 0

Find all values of x that satisfies the inequality (2x-3)/((x-2)(x-4))lt0

Find all possible values of (x^2+1)/(x^2-2) .

Find all values of x that satisfies the inequality (2x - 3)/((x - 2) (x - 4)) lt 0.

let f(x)=-x^3+(b^3-b^2+b-1)/(b^2+3b+2) if x is 0 to 1 and f(x)=2x-3 if x if 1 to 3 .All possible real values of b such that f (x) has the smallest value at x=1 ,are

The set of all real x satisfying the inequality (3-|x|)/(4-|x|) ge 0 is

The sum of all real values of X satisfying the equation (x^2-5x+5)^(x^2 + 4x -60) = 1 is:

Let (f(x+y)-f(x))/2=(f(y)-a)/2+x y for all real x and ydot If f(x) is differentiable and f^(prime)(0) exists for all real permissible value of a and is equal to sqrt(5a-1-a^2)dot Then a) f(x) is positive for all real x b) f(x) is negative for all real x c) f(x)=0 has real roots d) Nothing can be said about the sign of f(x)