What is the domain of f(x)=((2-x^2))/((x^2+2x-8)) ?

The domain of f(x)=((2-x^2))/((x^2+2x-8)) is x 2

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domain of f(x)=((2-x^2))/((x^2+2x-8))

domain

f (x) = \frac{( 2 - x ^{2} )}{( x ^{2} + 2 x - 8 )}

x < - 4 or - 4 < x < 2 or x > 2

Interval Notation

(- \infty, - 4) \cup (- 4, 2) \cup (2, \infty)

Solution steps

Find undefined (singularity) points:

x = 2, x = - 4

The function domain

x < - 4 or - 4 < x < 2 or x > 2

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