What is the domain of f(x)=(3-x^2)/(3x^2-5x-2) ?

The domain of f(x)=(3-x^2)/(3x^2-5x-2) is x 2

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domain of f(x)=(3-x^2)/(3x^2-5x-2)

domain

x < - \frac{1}{3} or - \frac{1}{3} < x < 2 or x > 2

Interval Notation

(- \infty, - \frac{1}{3}) \cup (- \frac{1}{3}, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = - \frac{1}{3}

The function domain

x < - \frac{1}{3} or - \frac{1}{3} < x < 2 or x > 2

What is the domain of f(x)=(3-x^2)/(3x^2-5x-2) ?
The domain of f(x)=(3-x^2)/(3x^2-5x-2) is x<-1/3 \lor-1/3 <x<2\lor x>2