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) = (5 - x) + (x^{2} - 4)

x \leq - 2 or 2 \leq 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

The function domain

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

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