What is the domain of f(x)=(x+2)/(sqrt(x+4)-3) ?

The domain of f(x)=(x+2)/(sqrt(x+4)-3) is -4 5

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domain of f(x)=(x+2)/(sqrt(x+4)-3)

domain

f (x) = \frac{x + 2}{x + 4 - 3}

- 4 \leq x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 4

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 4 \leq x < 5 or x > 5

What is the domain of f(x)=(x+2)/(sqrt(x+4)-3) ?
The domain of f(x)=(x+2)/(sqrt(x+4)-3) is -4<= x<5\lor x>5