What is the domain of f(x)=(sqrt(5-x))/(sqrt(x^2-4)) ?

The domain of f(x)=(sqrt(5-x))/(sqrt(x^2-4)) is x<-2\lor 2<x<= 5

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domain of f(x)=(sqrt(5-x))/(sqrt(x^2-4))

domain

f (x) = \frac{5 - x}{x ^{2} - 4}

x < - 2 or 2 < x \leq 5

Interval Notation

(- \infty, - 2) \cup (2, 5]

Solution steps

Find non-negative values for radicals:

x \leq - 2 or 2 \leq x \leq 5

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

x < - 2 or 2 < x \leq 5

f (x) = \frac{1}{x} - 3

f (x) = \frac{5 x}{2 x - 6}

f (x) = \frac{( x - 1 )}{x ^{2} + 3}

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

x^{2} - 5 x + 6

What is the domain of f(x)=(sqrt(5-x))/(sqrt(x^2-4)) ?
The domain of f(x)=(sqrt(5-x))/(sqrt(x^2-4)) is x<-2\lor 2<x<= 5