What is the domain of f(x)=(sqrt(6x-2))/(x^2-36) ?

The domain of f(x)=(sqrt(6x-2))/(x^2-36) is 1/3 6

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domain of f(x)=(sqrt(6x-2))/(x^2-36)

domain

f (x) = \frac{6 x - 2}{x ^{2} - 36}

\frac{1}{3} \leq x < 6 or x > 6

Interval Notation

[\frac{1}{3}, 6) \cup (6, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{3}

Find undefined (singularity) points:

x = 6, x = - 6

Combine real regions and undefined points for final function domain

\frac{1}{3} \leq x < 6 or x > 6

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

f (x) = \frac{2 x + 9}{x - 1}

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

\frac{4 x}{x + 3}

- 4 x + y = - 3

What is the domain of f(x)=(sqrt(6x-2))/(x^2-36) ?
The domain of f(x)=(sqrt(6x-2))/(x^2-36) is 1/3 <= x<6\lor x>6