What is the domain of f(x)=(2x)/(2x^3+5x^2-12x) ?

The domain of f(x)=(2x)/(2x^3+5x^2-12x) is x 3/2

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domain of f(x)=(2x)/(2x^3+5x^2-12x)

domain

x < - 4 or - 4 < x < 0 or 0 < x < \frac{3}{2} or x > \frac{3}{2}

Interval Notation

(- \infty, - 4) \cup (- 4, 0) \cup (0, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = \frac{3}{2}, x = - 4

The function domain

x < - 4 or - 4 < x < 0 or 0 < x < \frac{3}{2} or x > \frac{3}{2}

What is the domain of f(x)=(2x)/(2x^3+5x^2-12x) ?
The domain of f(x)=(2x)/(2x^3+5x^2-12x) is x<-4\lor-4<x<0\lor 0<x< 3/2 \lor x> 3/2