What is the domain of f(x)=sqrt(x+5)-(sqrt(7-x))/x ?

The domain of f(x)=sqrt(x+5)-(sqrt(7-x))/x is -5<= x<0\lor 0<x<= 7

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domain of f(x)=sqrt(x+5)-(sqrt(7-x))/x

domain

f (x) = x + 5 - \frac{7 - x}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 7

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

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

f (x) = 49 x^{3} - 3 x

f (x) = 8 x^{2} - 8

2 x^{2} - 17

y = 15

What is the domain of f(x)=sqrt(x+5)-(sqrt(7-x))/x ?
The domain of f(x)=sqrt(x+5)-(sqrt(7-x))/x is -5<= x<0\lor 0<x<= 7