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

The domain of f(x)= x/(x^2-|x|) is x 1

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domain of f(x)= x/(x^2-|x|)

domain

f (x) = \frac{x}{x ^{2} - ∣ x ∣}

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

Interval Notation

(- \infty, - 1) \cup (- 1, 0) \cup (0, 1) \cup (1, \infty)

Solution steps

Find undefined (singularity) points:

x = - 1, x = 0, x = 1

The function domain

x < - 1 or - 1 < x < 0 or 0 < x < 1 or x > 1

f (x) = \frac{x}{x + 3}

2 x^{3} - 24 x

f (x) = - 7 x + 3

3 x^{\frac{2}{3}} - 2 x

y = - 5 x - e^{- 5 x}

What is the domain of f(x)= x/(x^2-|x|) ?
The domain of f(x)= x/(x^2-|x|) is x<-1\lor-1<x<0\lor 0<x<1\lor x>1