What is the domain of f(x)=(4x+3)/(x^3-2x) ?

The domain of f(x)=(4x+3)/(x^3-2x) is x sqrt(2)

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domain of f(x)=(4x+3)/(x^3-2x)

domain

f (x) = \frac{4 x + 3}{x ^{3} - 2 x}

x < - 2 or - 2 < x < 0 or 0 < x < 2 or x > 2

Interval Notation

(- \infty, - 2) \cup (- 2, 0) \cup (0, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 2, x = 2

The function domain

x < - 2 or - 2 < x < 0 or 0 < x < 2 or x > 2

\frac{2 x + 3}{( 5 x - 1 ) ( x - 2 ) ^{0.5}}

f (x) = \frac{1}{x ^{2} + x - 12}

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

f (x) = \frac{20}{x ^{2} - 4 x - 4}

\frac{x + 11}{x - 9}

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