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Greatest Integer Function ( Inequation ) || Fractional Part Function

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The domain of f(x)=log_(10)x^(2)+[sin x]+{cos x} is where [.]is greatest integer function and {.} is fractional part function is

Solve (1)/(x)+(1)/([2x])={x}+(1)/(3) where [.] denotes the greatest integers function and {.} denotes fractional part function.

The sum of solutions of the equation 2[x] + x =6{x} is (where [.] denotes the greatest integer function and {.} denotes fractional part function)

Solve the following inequalities (where [*] denotes greatest integer function and {*} represent fractional part function) [2x^(2)-x]<1