What is the domain of (1+sqrt(-81x^2+1))/x ?

The domain of (1+sqrt(-81x^2+1))/x is -1/9 <= x<0\lor 0<x<= 1/9

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domain of (1+sqrt(-81x^2+1))/x

domain

\frac{1 + - 81 x ^{2} + 1}{x}

- \frac{1}{9} \leq x < 0 or 0 < x \leq \frac{1}{9}

Interval Notation

[- \frac{1}{9}, 0) \cup (0, \frac{1}{9}]

Solution steps

Find non-negative values for radicals:

- \frac{1}{9} \leq x \leq \frac{1}{9}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- \frac{1}{9} \leq x < 0 or 0 < x \leq \frac{1}{9}

f (x) = \frac{6}{x} - x - 7

2 - 3 cos (2 x)

x^{2} + 36 y^{2} = 36

6 sin (3 x - π)

f (x) = \frac{1}{x ^{3}}

What is the domain of (1+sqrt(-81x^2+1))/x ?
The domain of (1+sqrt(-81x^2+1))/x is -1/9 <= x<0\lor 0<x<= 1/9