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

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

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

domain

\frac{1}{x - 2} x + 4

- 4 \leq x < 2 or x > 2

Interval Notation

[- 4, 2) \cup (2, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- 4 \leq x < 2 or x > 2

f (x) = \frac{3}{x ^{2} - 4 x - 12}

\frac{x + 2}{2 x + 1}

f (x) = \frac{1}{( x - 3 ) ( 3 x + 1 )}

f (x) = \frac{3 x + 4}{( x + 4 ) ( x + 3 )}

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