What is the domain of \sqrt[4]{(x(x+7))/(x^2+5x+6)} ?

The domain of \sqrt[4]{(x(x+7))/(x^2+5x+6)} is x = 0

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domain of \sqrt[4]{(x(x+7))/(x^2+5x+6)}

domain

x \leq - 7 or - 3 < x < - 2 or x \geq 0

Interval Notation

(- \infty, - 7] \cup (- 3, - 2) \cup [0, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 7 or - 3 < x < - 2 or x \geq 0

Find undefined (singularity) points:

x = - 2, x = - 3

Combine real regions and undefined points for final function domain

x \leq - 7 or - 3 < x < - 2 or x \geq 0

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

f (x) = \frac{x ^{2} - 5 x - 14}{x - 6}

f (x) = - 3 x - 3 + 3

h (x) = \frac{2}{x + 2}

y = 9 x - 10

What is the domain of \sqrt[4]{(x(x+7))/(x^2+5x+6)} ?
The domain of \sqrt[4]{(x(x+7))/(x^2+5x+6)} is x<=-7\lor-3<x<-2\lor x>= 0