What is the domain of (sqrt(5-x))/(-5x) ?

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

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domain of (sqrt(5-x))/(-5x)

domain

\frac{5 - x}{- 5 x}

x < 0 or 0 < x \leq 5

Interval Notation

(- \infty, 0) \cup (0, 5]

Solution steps

Find non-negative values for radicals:

x \leq 5

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq 5

f (x) = \frac{3 - 2 x}{( x - 2 ) ( x + 3 )}

\frac{1}{64} 4^{5 x - 23}

f (x) = arctan (e^{x})

f (x) = - x^{2} + 5 x - 4

f (x) = \frac{2 x}{3 x ^{2} - 13 x - 10}

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