What is the domain of f(x)=(4x^2-8)/(x^3-5x^2-24x) ?

The domain of f(x)=(4x^2-8)/(x^3-5x^2-24x) is x 8

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domain of f(x)=(4x^2-8)/(x^3-5x^2-24x)

domain

f (x) = \frac{4 x ^{2} - 8}{x ^{3} - 5 x ^{2} - 24 x}

x < - 3 or - 3 < x < 0 or 0 < x < 8 or x > 8

Interval Notation

(- \infty, - 3) \cup (- 3, 0) \cup (0, 8) \cup (8, \infty)

Solution steps

Find undefined (singularity) points:

x = 0, x = - 3, x = 8

The function domain

x < - 3 or - 3 < x < 0 or 0 < x < 8 or x > 8

\frac{∣ x ∣}{x ^{2}}

f (x) = \frac{3 x}{x ^{2} - 64}

f (x) = 4 x - 1

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

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

What is the domain of f(x)=(4x^2-8)/(x^3-5x^2-24x) ?
The domain of f(x)=(4x^2-8)/(x^3-5x^2-24x) is x<-3\lor-3<x<0\lor 0<x<8\lor x>8