What is the domain of f(x)=(1-sqrt(9-x^2))/(|x-3|-1) ?

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

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domain of f(x)=(1-sqrt(9-x^2))/(|x-3|-1)

domain

f (x) = \frac{1 - 9 - x ^{2}}{∣ x - 3 ∣ - 1}

- 3 \leq x < 2 or 2 < x \leq 3

Interval Notation

[- 3, 2) \cup (2, 3]

Solution steps

Find non-negative values for radicals:

- 3 \leq x \leq 3

Find undefined (singularity) points:

x = 2, x = 4

Combine real regions and undefined points for final function domain

- 3 \leq x < 2 or 2 < x \leq 3

\frac{2 x + 1}{2 x + 4}

\frac{2 s + 3}{s ( 2 s + 1 )}

(x - 20)^{2}

y = lo g_{10} (7 + 6 x)

y = \frac{20}{10}

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