What is the domain of sqrt(x+4)-(sqrt(7-x))/x ?

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

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domain of sqrt(x+4)-(sqrt(7-x))/x

domain

x + 4 - \frac{7 - x}{x}

- 4 \leq x < 0 or 0 < x \leq 7

Interval Notation

[- 4, 0) \cup (0, 7]

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 7

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

- 4 \leq x < 0 or 0 < x \leq 7

f (x) = 2 x - 6 x^{2}

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

f (x) = (x + 4)^{\frac{1}{5}} + 3

F (X) = X^{5}

f (x) = \frac{7 + 2 x}{x}

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