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

The domain of f(x)=sqrt((\sqrt{x+1)-x)/x} is 0<x<= (sqrt(5)+1)/2

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domain of f(x)=sqrt((\sqrt{x+1)-x)/x}

domain

0 < x \leq \frac{5 + 1}{2}

Interval Notation

(0, \frac{5 + 1}{2}]

Solution steps

Find non-negative values for radicals:

0 < x \leq \frac{5 + 1}{2}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

0 < x \leq \frac{5 + 1}{2}

What is the domain of f(x)=sqrt((\sqrt{x+1)-x)/x} ?
The domain of f(x)=sqrt((\sqrt{x+1)-x)/x} is 0<x<= (sqrt(5)+1)/2