What is the domain of f(x)=sqrt(x+4)-(sqrt(8-x))/x ?

The domain of f(x)=sqrt(x+4)-(sqrt(8-x))/x is -4<= x<0\lor 0<x<= 8

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domain of f(x)=sqrt(x+4)-(sqrt(8-x))/x

domain

f (x) = x + 4 - \frac{8 - x}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 8

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=sqrt(x+4)-(sqrt(8-x))/x ?
The domain of f(x)=sqrt(x+4)-(sqrt(8-x))/x is -4<= x<0\lor 0<x<= 8