What is the domain of f(x)=sqrt((\sqrt{x^2-3x-4))/(sqrt(21)-\sqrt{x^2-4)}} ?

The domain of f(x)=sqrt((\sqrt{x^2-3x-4))/(sqrt(21)-\sqrt{x^2-4)}} is -5<x<=-2\lor 4<= x<5

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domain of f(x)=sqrt((\sqrt{x^2-3x-4))/(sqrt(21)-\sqrt{x^2-4)}}

domain

f (x) = \frac{x ^{2} - 3 x - 4}{21 - x ^{2} - 4}

- 5 < x \leq - 2 or 4 \leq x < 5

Interval Notation

(- 5, - 2] \cup [4, 5)

Solution steps

Find non-negative values for radicals:

- 5 < x \leq - 2 or 4 \leq x < 5

Find undefined (singularity) points:

x = 5, x = - 5

Combine real regions and undefined points for final function domain

- 5 < x \leq - 2 or 4 \leq x < 5

What is the domain of f(x)=sqrt((\sqrt{x^2-3x-4))/(sqrt(21)-\sqrt{x^2-4)}} ?
The domain of f(x)=sqrt((\sqrt{x^2-3x-4))/(sqrt(21)-\sqrt{x^2-4)}} is -5<x<=-2\lor 4<= x<5