What is the domain of sqrt(| 1/x+3|-4) ?

The domain of sqrt(| 1/x+3|-4) is -1/7 <= x<0\lor 0<x<= 1

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domain of sqrt(| 1/x+3|-4)

domain

\frac{1}{x} + 3 - 4

- \frac{1}{7} \leq x < 0 or 0 < x \leq 1

Interval Notation

[- \frac{1}{7}, 0) \cup (0, 1]

Solution steps

Find non-negative values for radicals:

- \frac{1}{7} \leq x < 0 or 0 < x \leq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- \frac{1}{7} \leq x < 0 or 0 < x \leq 1

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

f (x) = \frac{( x - 8 )}{( x + 8 )}

cos (2 x + 5)

\frac{x ^{2} + 5 x + 4}{x ^{2} + 3 x + 2}

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

What is the domain of sqrt(| 1/x+3|-4) ?
The domain of sqrt(| 1/x+3|-4) is -1/7 <= x<0\lor 0<x<= 1