What is the domain of f(x)=(sqrt(3x-1))/(x-5) ?

The domain of f(x)=(sqrt(3x-1))/(x-5) is 1/3 5

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domain of f(x)=(sqrt(3x-1))/(x-5)

domain

f (x) = \frac{3 x - 1}{x - 5}

\frac{1}{3} \leq x < 5 or x > 5

Interval Notation

[\frac{1}{3}, 5) \cup (5, \infty)

Solution steps

Find non-negative values for radicals:

x \geq \frac{1}{3}

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

\frac{1}{3} \leq x < 5 or x > 5

f (x) = x - 4 + 9 - x

\frac{x}{1 - 2 x}

\frac{x - 8}{x - 5}

- 2 cos (4 x)

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

What is the domain of f(x)=(sqrt(3x-1))/(x-5) ?
The domain of f(x)=(sqrt(3x-1))/(x-5) is 1/3 <= x<5\lor x>5