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

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

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

domain

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

- 4 \leq x < 0 or 0 < x \leq 1

Interval Notation

[- 4, 0) \cup (0, 1]

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 1

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 4 \leq x < 0 or 0 < x \leq 1

f (x) = \frac{8}{x - 6}

\frac{x + 8}{x ^{2} - 4}

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

cos (2 x + 5)

f (x) = 2 (x + 3)^{2} - 18

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