What is the domain of f(x)=(sqrt(5+x))/(2-x) ?

The domain of f(x)=(sqrt(5+x))/(2-x) is -5 2

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domain of f(x)=(sqrt(5+x))/(2-x)

domain

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

- 5 \leq x < 2 or x > 2

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

x = 2

Combine real regions and undefined points for final function domain

- 5 \leq x < 2 or x > 2

What is the domain of f(x)=(sqrt(5+x))/(2-x) ?
The domain of f(x)=(sqrt(5+x))/(2-x) is -5<= x<2\lor x>2