What is the domain of f(x)=sqrt((100-x^2)/(x^2+4x-21)) ?

The domain of f(x)=sqrt((100-x^2)/(x^2+4x-21)) is -10<= x<-7\lor 3<x<= 10

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domain of f(x)=sqrt((100-x^2)/(x^2+4x-21))

domain

f (x) = \frac{100 - x ^{2}}{x ^{2} + 4 x - 21}

- 10 \leq x < - 7 or 3 < x \leq 10

Interval Notation

[- 10, - 7) \cup (3, 10]

Solution steps

Find non-negative values for radicals:

- 10 \leq x < - 7 or 3 < x \leq 10

Find undefined (singularity) points:

x = 3, x = - 7

Combine real regions and undefined points for final function domain

- 10 \leq x < - 7 or 3 < x \leq 10

f (x) = \frac{x + 3}{x ^{2} - 16}

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

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

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

f (x) = ∣ x - 1 ∣ + 2

What is the domain of f(x)=sqrt((100-x^2)/(x^2+4x-21)) ?
The domain of f(x)=sqrt((100-x^2)/(x^2+4x-21)) is -10<= x<-7\lor 3<x<= 10