What is the domain of f(x)=(sqrt(5-x))/(sqrt(x^2-9)) ?

The domain of f(x)=(sqrt(5-x))/(sqrt(x^2-9)) is x<-3\lor 3<x<= 5

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domain of f(x)=(sqrt(5-x))/(sqrt(x^2-9))

domain

f (x) = \frac{5 - x}{x ^{2} - 9}

x < - 3 or 3 < x \leq 5

Interval Notation

(- \infty, - 3) \cup (3, 5]

Solution steps

Find non-negative values for radicals:

x \leq - 3 or 3 \leq x \leq 5

Find undefined (singularity) points:

x = 3, x = - 3

Combine real regions and undefined points for final function domain

x < - 3 or 3 < x \leq 5

(5, - 6), (- 1, 2)

f (x) = 5 + \frac{4}{x}

x - 3 y = 12

f (x) = \frac{x + 8}{x ^{2} - 1}

What is the domain of f(x)=(sqrt(5-x))/(sqrt(x^2-9)) ?
The domain of f(x)=(sqrt(5-x))/(sqrt(x^2-9)) is x<-3\lor 3<x<= 5