If `x=4/9` satisfies the equation `(log)_a(x^2-x+2)>(log)_a(-x^2+2x+3),` then the sum of all possible distinct values of `[x]` is (where`[dot]` represetns the greatest integer function) ___

If alpha is an integer satisfying |alpha|lt=4-|[x]|, where x is a real number for which 2xtan^(-1)x is greater than or equal to ln(1+x^2), then the number of maximum possible values of alpha (where [.] represents the greatest integer function) is_____

Evaluate lim_(xto2^(+)) ([x-2])/(log(x-2)), where [.] represents the greatest integer function.

f(x)=sin^-1[log_2(x^2/2)] where [ . ] denotes the greatest integer function.

Find the value of x in [1,3] where the function [x^2+1]([dot] represents the greatest integer function) is discontinuous.

If f(x)=(sin([x]pi))/(x^2+x+1) , where [dot] denotes the greatest integer function, then

The domain of the function f(x)=log_e {sgn(9-x^2)}+sqrt([x]^3-4[x]) (where [] represents the greatest integer function is

Domain of f(x)=log(x^2+5x+6)/([x]-1) where [.] denotes greatest integer function:

Find the domain and range of f(x)=log[ cos|x|+1/2] ,where [.] denotes the greatest integer function.

Find the values of x graphically which satisfy, -1le[x]-x^(2)+4le2 , where [.] denotes the greatest integer function.

The domain of the function sqrt(log_(1/3) log_4 ([x]^2 - 5 )) is (where [x] denotes greatest integer function)