What is the domain of f(x)=sqrt((x+1)/(x^2)-1) ?

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

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domain of f(x)=sqrt((x+1)/(x^2)-1)

domain

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

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

Interval Notation

[\frac{1 - 5}{2}, 0) \cup (0, \frac{1 + 5}{2}]

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

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