What is the domain of g(x)=(sqrt(2+x))/(3-x) ?

The domain of g(x)=(sqrt(2+x))/(3-x) is -2 3

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domain of g(x)=(sqrt(2+x))/(3-x)

domain

g (x) = \frac{2 + x}{3 - x}

- 2 \leq x < 3 or x > 3

Interval Notation

[- 2, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 2 \leq x < 3 or x > 3

What is the domain of g(x)=(sqrt(2+x))/(3-x) ?
The domain of g(x)=(sqrt(2+x))/(3-x) is -2<= x<3\lor x>3