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

The domain of f(x)=(sqrt(1-3x))/x is x<0\lor 0<x<= 1/3

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

domain

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

x < 0 or 0 < x \leq \frac{1}{3}

Interval Notation

(- \infty, 0) \cup (0, \frac{1}{3}]

Solution steps

Find non-negative values for radicals:

x \leq \frac{1}{3}

Find undefined (singularity) points:

x = 0

Combine real regions and undefined points for final function domain

x < 0 or 0 < x \leq \frac{1}{3}

y = 2 x + 2

5 x + 1

x^{2} - 5 x

f (x) = - x^{2} + 8 x - 25

y = \frac{3}{5} x - 6

What is the domain of f(x)=(sqrt(1-3x))/x ?
The domain of f(x)=(sqrt(1-3x))/x is x<0\lor 0<x<= 1/3