What is the domain of f(x)=(sqrt(3+x))/(7-x) ?

The domain of f(x)=(sqrt(3+x))/(7-x) is -3 7

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domain of f(x)=(sqrt(3+x))/(7-x)

domain

f (x) = \frac{3 + x}{7 - x}

- 3 \leq x < 7 or x > 7

Interval Notation

[- 3, 7) \cup (7, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 7

Combine real regions and undefined points for final function domain

- 3 \leq x < 7 or x > 7

What is the domain of f(x)=(sqrt(3+x))/(7-x) ?
The domain of f(x)=(sqrt(3+x))/(7-x) is -3<= x<7\lor x>7