What is the domain of f(x)=(sqrt(16-x^2))/(x-3) ?

The domain of f(x)=(sqrt(16-x^2))/(x-3) is -4<= x<3\lor 3<x<= 4

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domain of f(x)=(sqrt(16-x^2))/(x-3)

domain

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

- 4 \leq x < 3 or 3 < x \leq 4

Interval Notation

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 4

Find undefined (singularity) points:

x = 3

Combine real regions and undefined points for final function domain

- 4 \leq x < 3 or 3 < x \leq 4

f (x) = \frac{x ^{2} - 2 x - 24}{x ^{2} - 25}

f (x) = \frac{x + 5}{x ^{2} - 7 x + 10}

- \frac{x + 2}{4}

f (x) = \frac{1}{5 x - 15}

f (x) = 2 (x - 1)^{2} - 3

What is the domain of f(x)=(sqrt(16-x^2))/(x-3) ?
The domain of f(x)=(sqrt(16-x^2))/(x-3) is -4<= x<3\lor 3<x<= 4