What is the domain of (sqrt(x+8)+2)/(x+2) ?

The domain of (sqrt(x+8)+2)/(x+2) is -8 -2

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domain of (sqrt(x+8)+2)/(x+2)

domain

\frac{x + 8 + 2}{x + 2}

- 8 \leq x < - 2 or x > - 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 8

Find undefined (singularity) points:

x = - 2

Combine real regions and undefined points for final function domain

- 8 \leq x < - 2 or x > - 2

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

f (x) = \frac{5 x}{2 x + 3}

f (x) = x^{2}, [0, \infty]

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

f (x) = x^{5}

What is the domain of (sqrt(x+8)+2)/(x+2) ?
The domain of (sqrt(x+8)+2)/(x+2) is -8<= x<-2\lor x>-2