What is the domain of f(x)=((x^3+3x^2))/((7x^2-2)) ?

The domain of f(x)=((x^3+3x^2))/((7x^2-2)) is x sqrt(2/7)

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domain of f(x)=((x^3+3x^2))/((7x^2-2))

domain

x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{2}{7} or x > \frac{2}{7}

Interval Notation

(- \infty, - \frac{2}{7}) \cup (- \frac{2}{7}, \frac{2}{7}) \cup (\frac{2}{7}, \infty)

Solution steps

Find undefined (singularity) points:

x = \frac{2}{7}, x = - \frac{2}{7}

The function domain

x < - \frac{2}{7} or - \frac{2}{7} < x < \frac{2}{7} or x > \frac{2}{7}

What is the domain of f(x)=((x^3+3x^2))/((7x^2-2)) ?
The domain of f(x)=((x^3+3x^2))/((7x^2-2)) is x<-sqrt(2/7)\lor-sqrt(2/7)<x<sqrt(2/7)\lor x>sqrt(2/7)