What is the domain of y=(x+3)/(12-sqrt(x^2-25)) ?

The domain of y=(x+3)/(12-sqrt(x^2-25)) is x 13

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domain of y=(x+3)/(12-sqrt(x^2-25))

domain

y = \frac{x + 3}{12 - x ^{2} - 25}

x < - 13 or - 13 < x \leq - 5 or 5 \leq x < 13 or x > 13

Interval Notation

(- \infty, - 13) \cup (- 13, - 5] \cup [5, 13) \cup (13, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 5 or x \geq 5

Find undefined (singularity) points:

x = 13, x = - 13

Combine real regions and undefined points for final function domain

x < - 13 or - 13 < x \leq - 5 or 5 \leq x < 13 or x > 13

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

f (x) = lo g_{10} (∣ x ∣)

f (x) = \frac{3 x + 2}{x ^{2} - 4}

g (x) = \frac{1}{x - 9}

f (x) = - (x + 2)^{5} (x - 4)^{4}

What is the domain of y=(x+3)/(12-sqrt(x^2-25)) ?
The domain of y=(x+3)/(12-sqrt(x^2-25)) is x<-13\lor-13<x<=-5\lor 5<= x<13\lor x>13