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

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

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

domain

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

x \geq 3

Interval Notation

[3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq 3

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x \geq 3

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

\frac{x}{- 8 x + 81}

- 4 x + 2

- 4 x + 6

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

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