What is the domain of f(x)=(sqrt(9-x^2))/(x-1) ?

The domain of f(x)=(sqrt(9-x^2))/(x-1) is -3<= x<1\lor 1<x<= 3

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domain of f(x)=(sqrt(9-x^2))/(x-1)

domain

f (x) = \frac{9 - x ^{2}}{x - 1}

- 3 \leq x < 1 or 1 < x \leq 3

Interval Notation

[- 3, 1) \cup (1, 3]

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq 3

Find undefined (singularity) points:

x = 1

Combine real regions and undefined points for final function domain

- 3 \leq x < 1 or 1 < x \leq 3

What is the domain of f(x)=(sqrt(9-x^2))/(x-1) ?
The domain of f(x)=(sqrt(9-x^2))/(x-1) is -3<= x<1\lor 1<x<= 3