What is the domain of f(x)=(5x)/(|x|-2) ?

The domain of f(x)=(5x)/(|x|-2) is x 2

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domain of f(x)=(5x)/(|x|-2)

domain

f (x) = \frac{5 x}{∣ x ∣ - 2}

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

Interval Notation

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

Solution steps

Find undefined (singularity) points:

x = - 2, x = 2

The function domain

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

f (x) = 120 x - 3 x^{2}

f (x) = 2^{3} x

(x - 10) (x + 2)

\frac{- 3 x + 5}{2}, - 1 \leq x < 4

\frac{1}{1 + \frac{1}{1 + \frac{1}{x}}}

What is the domain of f(x)=(5x)/(|x|-2) ?
The domain of f(x)=(5x)/(|x|-2) is x<-2\lor-2<x<2\lor x>2