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

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

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

domain

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

y = - 2 x - 4

f (x) = x^{6}

f (x) = \frac{4 x + 3}{2 x - 6}

(- 4, 6), (0, - 10)

f (x) = 3 (x - 41)

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