What is the domain of f(x)=(2-sqrt(4-x))/x ?

The domain of f(x)=(2-sqrt(4-x))/x is x<0\lor 0<x<= 4

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domain of f(x)=(2-sqrt(4-x))/x

domain

f (x) = \frac{2 - 4 - x}{x}

x < 0 or 0 < x \leq 4

Interval Notation

(- \infty, 0) \cup (0, 4]

Solution steps

Find non-negative values for radicals:

x \leq 4

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq 4

f (x) = \frac{2}{5} x - 6

f (x) = 4 x - 9

f (x) = \frac{x + 1}{x ^{2} - 1}

sin (7 x)

f (x) = \frac{4}{x - 9}

What is the domain of f(x)=(2-sqrt(4-x))/x ?
The domain of f(x)=(2-sqrt(4-x))/x is x<0\lor 0<x<= 4