What is the domain of f(x)=(x^3-2x)/(6x^3+7x^2-5x) ?

The domain of f(x)=(x^3-2x)/(6x^3+7x^2-5x) is x 1/2

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domain of f(x)=(x^3-2x)/(6x^3+7x^2-5x)

domain

f (x) = \frac{x ^{3} - 2 x}{6 x ^{3} + 7 x ^{2} - 5 x}

x < - \frac{5}{3} or - \frac{5}{3} < x < 0 or 0 < x < \frac{1}{2} or x > \frac{1}{2}

Interval Notation

(- \infty, - \frac{5}{3}) \cup (- \frac{5}{3}, 0) \cup (0, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = \frac{1}{2}, x = - \frac{5}{3}

The function domain

x < - \frac{5}{3} or - \frac{5}{3} < x < 0 or 0 < x < \frac{1}{2} or x > \frac{1}{2}

f (x) = \frac{( 7 x + 8 )}{x - 3}

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

f (x) = - 5 + 4 x

x + 3

\frac{1}{1 + x ^{2}}

What is the domain of f(x)=(x^3-2x)/(6x^3+7x^2-5x) ?
The domain of f(x)=(x^3-2x)/(6x^3+7x^2-5x) is x<-5/3 \lor-5/3 <x<0\lor 0<x< 1/2 \lor x> 1/2