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

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

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

domain

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

- 2 \leq x < 4 or x > 4

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 2

Find undefined (singularity) points:

x = 4

Combine real regions and undefined points for final function domain

- 2 \leq x < 4 or x > 4

f (x) = \frac{x + 1}{x ^{2} - 4}

(- 4.5) (0.9)

f (x) = - 3 - x - 2

f (x) = \frac{x ^{2} + 3 x}{x ^{2} + x - 6}

(4, 0), (20, 25)

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