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

The domain of f(x)=(x^3-2x^2-3x)/(2x^2-x-6) is x 2

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

domain

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

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

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

The function domain

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

f (x) = (x + 3)^{2} + (y + 6)^{2} = 16

f (x) = \frac{x ^{2} + 2 x - 8}{x + 2}

f (x) = ln ∣ x - 1 ∣

f (x) = \frac{1}{5 - x}

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

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