What is the domain of (sqrt(16-x^2)-4)/(2-|x-3|) ?

The domain of (sqrt(16-x^2)-4)/(2-|x-3|) is -4<= x<1\lor 1<x<= 4

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domain of (sqrt(16-x^2)-4)/(2-|x-3|)

domain

\frac{16 - x ^{2} - 4}{2 - ∣ x - 3 ∣}

- 4 \leq x < 1 or 1 < x \leq 4

Interval Notation

[- 4, 1) \cup (1, 4]

Solution steps

Find non-negative values for radicals:

- 4 \leq x \leq 4

Find undefined (singularity) points:

x = 1, x = 5

Combine real regions and undefined points for final function domain

- 4 \leq x < 1 or 1 < x \leq 4

f (x) = 2 - 11 x

\frac{5 x - 6}{6 x + 1}

f (x) = lo g_{5} (\frac{x ^{2} - 9}{x + 3})

\frac{ln ( 3 \frac{x}{10} ) - 4}{3}

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

What is the domain of (sqrt(16-x^2)-4)/(2-|x-3|) ?
The domain of (sqrt(16-x^2)-4)/(2-|x-3|) is -4<= x<1\lor 1<x<= 4