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

3 x^{3} - 9 x + 1

3 cos (4 x)

f (x) = x^{4} - 18 x^{2}

f (x) = x^{3} - 3 x^{2} - 13 x + 15

f (x) = x^{\frac{5}{2}} - 8 x^{2}

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