What is the domain of f(x)=(2x+7)/(x^3-5x^2-4x+20) ?

The domain of f(x)=(2x+7)/(x^3-5x^2-4x+20) is x 5

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domain of f(x)=(2x+7)/(x^3-5x^2-4x+20)

domain

f (x) = \frac{2 x + 7}{x ^{3} - 5 x ^{2} - 4 x + 20}

x < - 2 or - 2 < x < 2 or 2 < x < 5 or x > 5

Interval Notation

(- \infty, - 2) \cup (- 2, 2) \cup (2, 5) \cup (5, \infty)

Solution steps

Find undefined (singularity) points:

x = 5, x = - 2, x = 2

The function domain

x < - 2 or - 2 < x < 2 or 2 < x < 5 or x > 5

f (x) = \frac{x - 2}{1 - 3 x}

sin (x + \frac{3 π}{2})

4 x^{2} + 2

\frac{3 x + 1}{x - 2}

f (x) = \frac{- x ^{6} + 6 x}{10}

What is the domain of f(x)=(2x+7)/(x^3-5x^2-4x+20) ?
The domain of f(x)=(2x+7)/(x^3-5x^2-4x+20) is x<-2\lor-2<x<2\lor 2<x<5\lor x>5