What is the domain of f(x)=(sqrt(4+x))/(6-x) ?

The domain of f(x)=(sqrt(4+x))/(6-x) is -4 6

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domain of f(x)=(sqrt(4+x))/(6-x)

domain

f (x) = \frac{4 + x}{6 - x}

- 4 \leq x < 6 or x > 6

Interval Notation

[- 4, 6) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

- 4 \leq x < 6 or x > 6

cr i t i c a l 2 x + \frac{1936}{x}

f (x) = 4 - x^{2}

in t erce pt s \frac{1}{x ^{2} - 4}

d i s t an ce (4, 2), (8, 5)

in v erse \frac{x + 3}{x - 5}

What is the domain of f(x)=(sqrt(4+x))/(6-x) ?
The domain of f(x)=(sqrt(4+x))/(6-x) is -4<= x<6\lor x>6