What is the domain of f(x)=sqrt(x-\sqrt{1-x^2)} ?

The domain of f(x)=sqrt(x-\sqrt{1-x^2)} is sqrt(1/2)<= x<= 1

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domain of f(x)=sqrt(x-\sqrt{1-x^2)}

domain

f (x) = x - 1 - x^{2}

\frac{1}{2} \leq x \leq 1

Interval Notation

[\frac{1}{2}, 1]

Solution steps

Find non-negative values for radicals:

\frac{1}{2} \leq x \leq 1

The function domain

\frac{1}{2} \leq x \leq 1

What is the domain of f(x)=sqrt(x-\sqrt{1-x^2)} ?
The domain of f(x)=sqrt(x-\sqrt{1-x^2)} is sqrt(1/2)<= x<= 1