What is the domain of f(x)=(3x-1)/(sqrt(-1+9x^2)) ?

The domain of f(x)=(3x-1)/(sqrt(-1+9x^2)) is x 1/3

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domain of f(x)=(3x-1)/(sqrt(-1+9x^2))

domain

f (x) = \frac{3 x - 1}{- 1 + 9 x ^{2}}

x < - \frac{1}{3} or x > \frac{1}{3}

Interval Notation

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

Solution steps

Find non-negative values for radicals:

x \leq - \frac{1}{3} or x \geq \frac{1}{3}

Find undefined (singularity) points:

x = \frac{1}{3}, x = - \frac{1}{3}

Combine real regions and undefined points for final function domain

x < - \frac{1}{3} or x > \frac{1}{3}

What is the domain of f(x)=(3x-1)/(sqrt(-1+9x^2)) ?
The domain of f(x)=(3x-1)/(sqrt(-1+9x^2)) is x<-1/3 \lor x> 1/3