What is the domain of f(x)=(sqrt(x+5))/(x-3) ?

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

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domain of f(x)=(sqrt(x+5))/(x-3)

domain

f (x) = \frac{x + 5}{x - 3}

- 5 \leq x < 3 or x > 3

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 5

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 5 \leq x < 3 or x > 3

(2, 4), (1, - 3)

f (x) = \frac{3}{\frac{3}{x}}

y - 3 = 3 (x + 1)

f (x) = \frac{x + 1}{3}

x + 5 = 0

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