What is the domain of 1/((2x^{(3))-7x)} ?

The domain of 1/((2x^{(3))-7x)} is x sqrt(7/2)

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domain of 1/((2x^{(3))-7x)}

domain

\frac{1}{( 2 x ^{(3)} - 7 x )}

x < - \frac{7}{2} or - \frac{7}{2} < x < 0 or 0 < x < \frac{7}{2} or x > \frac{7}{2}

Interval Notation

(- \infty, - \frac{7}{2}) \cup (- \frac{7}{2}, 0) \cup (0, \frac{7}{2}) \cup (\frac{7}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - \frac{7}{2}, x = \frac{7}{2}

The function domain

x < - \frac{7}{2} or - \frac{7}{2} < x < 0 or 0 < x < \frac{7}{2} or x > \frac{7}{2}

What is the domain of 1/((2x^{(3))-7x)} ?
The domain of 1/((2x^{(3))-7x)} is x<-sqrt(7/2)\lor-sqrt(7/2)<x<0\lor 0<x<sqrt(7/2)\lor x>sqrt(7/2)