What is the domain of y=(sqrt(36-x^2)+3)/(x-5) ?

The domain of y=(sqrt(36-x^2)+3)/(x-5) is -6<= x<5\lor 5<x<= 6

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domain of y=(sqrt(36-x^2)+3)/(x-5)

domain

y = \frac{36 - x ^{2} + 3}{x - 5}

- 6 \leq x < 5 or 5 < x \leq 6

Interval Notation

[- 6, 5) \cup (5, 6]

Solution steps

Find non-negative values for radicals:

- 6 \leq x \leq 6

Find undefined (singularity) points:

x = 5

Combine real regions and undefined points for final function domain

- 6 \leq x < 5 or 5 < x \leq 6

3 x^{3} - 6 x^{2}

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

3 x - 5 3 x + 5

4 x 8 - x

f (x) = \frac{x ^{2} - 1}{∣ x - 2 ∣}

What is the domain of y=(sqrt(36-x^2)+3)/(x-5) ?
The domain of y=(sqrt(36-x^2)+3)/(x-5) is -6<= x<5\lor 5<x<= 6