What is the domain of f(x)=(sqrt(x+3))/(x^2-5) ?

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

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domain of f(x)=(sqrt(x+3))/(x^2-5)

domain

f (x) = \frac{x + 3}{x ^{2} - 5}

- 3 \leq x < - 5 or - 5 < x < 5 or x > 5

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \geq - 3

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

- 3 \leq x < - 5 or - 5 < x < 5 or x > 5

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

f (x) = x^{3} - x + 1

\frac{\frac{x}{x + 1}}{\frac{1}{x}}

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

f (x) = cos (x) - 1

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