What is the domain of sqrt(x+8)-(sqrt(2-x))/x ?

The domain of sqrt(x+8)-(sqrt(2-x))/x is -8<= x<0\lor 0<x<= 2

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domain of sqrt(x+8)-(sqrt(2-x))/x

domain

x + 8 - \frac{2 - x}{x}

- 8 \leq x < 0 or 0 < x \leq 2

Interval Notation

[- 8, 0) \cup (0, 2]

Solution steps

Find non-negative values for radicals:

- 8 \leq x \leq 2

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 8 \leq x < 0 or 0 < x \leq 2

f (x) = - 5 t^{2} + 10 t - 3

f (x) = \frac{1 + 3 x ^{5}}{2 - x ^{5}}

ln (11 x^{2} + 3)

f (x) = \frac{5}{\frac{x}{x + 5}}

f (x) = \frac{1}{2 x - 3}

What is the domain of sqrt(x+8)-(sqrt(2-x))/x ?
The domain of sqrt(x+8)-(sqrt(2-x))/x is -8<= x<0\lor 0<x<= 2