What is the domain of f(x)=sqrt((-x+5)/(x^2-1)) ?

The domain of f(x)=sqrt((-x+5)/(x^2-1)) is x<-1\lor 1<x<= 5

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domain of f(x)=sqrt((-x+5)/(x^2-1))

domain

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

x < - 1 or 1 < x \leq 5

Interval Notation

(- \infty, - 1) \cup (1, 5]

Solution steps

Find non-negative values for radicals:

x < - 1 or 1 < x \leq 5

Find undefined (singularity) points:

x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 1 or 1 < x \leq 5

a sy m pt o t es f (x) = 6^{x - 2} + 1

r an g e x + 4

in t erce pt s 2 x^{3} - 4 x^{2} - 14 x + 28

d o main \frac{4 - x ^{2}}{x + 1}

in v erse f (x) = 8 x

What is the domain of f(x)=sqrt((-x+5)/(x^2-1)) ?
The domain of f(x)=sqrt((-x+5)/(x^2-1)) is x<-1\lor 1<x<= 5