What is the domain of f(x)=1+e^{((x^2)/(|x|-2))} ?

The domain of f(x)=1+e^{((x^2)/(|x|-2))} is x 2

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domain of f(x)=1+e^{((x^2)/(|x|-2))}

domain

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

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