What is the domain of g(x)=(sqrt(4+x))/(8-x) ?

The domain of g(x)=(sqrt(4+x))/(8-x) is -4 8

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domain of g(x)=(sqrt(4+x))/(8-x)

domain

g (x) = \frac{4 + x}{8 - x}

- 4 \leq x < 8 or x > 8

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 8

Combine real regions and undefined points for final function domain

- 4 \leq x < 8 or x > 8

cr i t i c a l x^{3} - 27 x

in v erse f (x) = \frac{x}{x + 20}

d o main f (x) = 3^{x} x - 2

d o main f (x) = 6 - t

e x t re m e f (x) = x^{3} + 12 x^{2} + 5

What is the domain of g(x)=(sqrt(4+x))/(8-x) ?
The domain of g(x)=(sqrt(4+x))/(8-x) is -4<= x<8\lor x>8