What is the domain of f(x)= 1/(x-2sqrt(x)) ?

The domain of f(x)= 1/(x-2sqrt(x)) is 0 4

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domain of f(x)= 1/(x-2sqrt(x))

domain

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

0 < x < 4 or x > 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 4, x = 0

Combine real regions and undefined points for final function domain

0 < x < 4 or x > 4

f (x) = \frac{x ^{2} + 9 - x}{x}

f (x) = \frac{5 x + 8}{3 x - 5}

f (x) = \frac{4 x ^{2} - 9}{x ^{2} - 25}

- x + 9 x - 20

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

What is the domain of f(x)= 1/(x-2sqrt(x)) ?
The domain of f(x)= 1/(x-2sqrt(x)) is 0<x<4\lor x>4