What is the domain of f(x)=(sqrt(x+4))/(x-5) ?

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

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domain of f(x)=(sqrt(x+4))/(x-5)

domain

f (x) = \frac{x + 4}{x - 5}

- 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

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

9 - x^{2} - x + 2

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

x - 4

f (x) = x - 2 y = - 4

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