What is the domain of f(x)=sqrt(x+5)-(sqrt(4-x))/x ?

The domain of f(x)=sqrt(x+5)-(sqrt(4-x))/x is -5<= x<0\lor 0<x<= 4

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domain of f(x)=sqrt(x+5)-(sqrt(4-x))/x

domain

f (x) = x + 5 - \frac{4 - x}{x}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 4

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

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

(- \frac{1}{2}, 0), (0, \frac{1}{4})

f (x) = 12 x - 3 x^{2}

y = \frac{x + 1}{6}

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

What is the domain of f(x)=sqrt(x+5)-(sqrt(4-x))/x ?
The domain of f(x)=sqrt(x+5)-(sqrt(4-x))/x is -5<= x<0\lor 0<x<= 4