What is the domain of y=(x+6)/(15-sqrt(x^2-64)) ?

The domain of y=(x+6)/(15-sqrt(x^2-64)) is x 17

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domain of y=(x+6)/(15-sqrt(x^2-64))

domain

y = \frac{x + 6}{15 - x ^{2} - 64}

x < - 17 or - 17 < x \leq - 8 or 8 \leq x < 17 or x > 17

Interval Notation

(- \infty, - 17) \cup (- 17, - 8] \cup [8, 17) \cup (17, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 8 or x \geq 8

Find undefined (singularity) points:

x = 17, x = - 17

Combine real regions and undefined points for final function domain

x < - 17 or - 17 < x \leq - 8 or 8 \leq x < 17 or x > 17

(x + 3) 2 - 2

7 x^{2} - 10 x + 5

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

y = \frac{- ∣ x ∣ + 4}{x ^{2} + x}

f (x) = - 2 x^{2} - 12 x + 13

What is the domain of y=(x+6)/(15-sqrt(x^2-64)) ?
The domain of y=(x+6)/(15-sqrt(x^2-64)) is x<-17\lor-17<x<=-8\lor 8<= x<17\lor x>17