What is the domain of f(x)=(sqrt(9+x))/(6-x) ?

The domain of f(x)=(sqrt(9+x))/(6-x) is -9 6

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domain of f(x)=(sqrt(9+x))/(6-x)

domain

f (x) = \frac{9 + x}{6 - x}

- 9 \leq x < 6 or x > 6

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 9

Find undefined (singularity) points:

x = 6

Combine real regions and undefined points for final function domain

- 9 \leq x < 6 or x > 6

What is the domain of f(x)=(sqrt(9+x))/(6-x) ?
The domain of f(x)=(sqrt(9+x))/(6-x) is -9<= x<6\lor x>6