What is the domain of sqrt(x+3)-(sqrt(7-x))/x ?

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

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domain of sqrt(x+3)-(sqrt(7-x))/x

domain

x + 3 - \frac{7 - x}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq 7

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

2 x - 1

y = 9 - x

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

x + 5 y = 15

10

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