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

f (x) = \frac{x + 1 - x}{x}

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}

f (x) = \frac{x}{1 - 6 x}

\frac{3}{x - 7}

f (x) = - 4 x^{2} + 6

(5 x + 6) + (1 - 8 x) x

f (x) = \frac{x - 7}{x ^{2} - 1}

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