What is the domain of f(x)=(sqrt(25-x^2))/(x^2-16) ?

The domain of f(x)=(sqrt(25-x^2))/(x^2-16) is -5<= x<-4\lor-4<x<4\lor 4<x<= 5

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domain of f(x)=(sqrt(25-x^2))/(x^2-16)

domain

f (x) = \frac{25 - x ^{2}}{x ^{2} - 16}

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

Interval Notation

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

Solution steps

Find non-negative values for radicals:

- 5 \leq x \leq 5

Find undefined (singularity) points:

x = 4, x = - 4

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=(sqrt(25-x^2))/(x^2-16) ?
The domain of f(x)=(sqrt(25-x^2))/(x^2-16) is -5<= x<-4\lor-4<x<4\lor 4<x<= 5