Find the domain of the real valued function

f(x)=√log_0.3 (x-x²)

Dear sindhuja

f(x)=√log_0.3 (x-x²)

term inside the rute must be positive

log_0.3 (x-x²)≥0

so   here base 0.3<1

 so   0 <x-x² ≤ 1

   x-x² >0

  x(1-x)>0

    x<0  or x>1

and  x-x² ≤ 1

        x² -x +1 ≤0

    it is always true

 so domain will be x<0  or x>1

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