What is the domain of 1/(sqrt(x)(x^2-4)) ?

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

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domain of 1/(sqrt(x)(x^2-4))

domain

\frac{1}{x ( x ^{2} - 4 )}

0 < x < 2 or x > 2

Interval Notation

(0, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 0

Find undefined (singularity) points:

x = 0, x = 2

Combine real regions and undefined points for final function domain

0 < x < 2 or x > 2

f (x) = x x - 1

f (x) = \frac{12}{x ^{2} - 25}

f (x) = lo g_{10} (lo g_{∣ s i n (x) ∣} (x^{2} - 8 x + 23) - \frac{3}{lo g _{2} ( ∣ sin ( x ) ∣ )})

\frac{8 x + 9}{7 x - 8}

f (x) = \frac{x + 5}{( x - 7 ) ( x - 2 )}

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