What is the domain of f(x)=sqrt((4-x)/(|x|-1)) ?

The domain of f(x)=sqrt((4-x)/(|x|-1)) is x<-1\lor 1<x<= 4

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domain of f(x)=sqrt((4-x)/(|x|-1))

domain

f (x) = \frac{4 - x}{∣ x ∣ - 1}

x < - 1 or 1 < x \leq 4

Interval Notation

(- \infty, - 1) \cup (1, 4]

Solution steps

Find non-negative values for radicals:

x < - 1 or 1 < x \leq 4

Find undefined (singularity) points:

x = - 1, x = 1

Combine real regions and undefined points for final function domain

x < - 1 or 1 < x \leq 4

\frac{1}{x ( x - 1 )}

f (x) = \frac{2 x}{5 x - 1}

\frac{x ^{2} + 7 x + 12}{x ^{2} - 3 x - 10}

f (x) = cosh^{2} (ln (x) - 1)

What is the domain of f(x)=sqrt((4-x)/(|x|-1)) ?
The domain of f(x)=sqrt((4-x)/(|x|-1)) is x<-1\lor 1<x<= 4