What is the domain of 1/(sqrt(x^4-10x^2+9)) ?

The domain of 1/(sqrt(x^4-10x^2+9)) is x 3

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domain of 1/(sqrt(x^4-10x^2+9))

domain

\frac{1}{x ^{4} - 10 x ^{2} + 9}

x < - 3 or - 1 < x < 1 or x > 3

Interval Notation

(- \infty, - 3) \cup (- 1, 1) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 3 or - 1 \leq x \leq 1 or x \geq 3

Find undefined (singularity) points:

x = 3, x = - 3, x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 3 or - 1 < x < 1 or x > 3

\frac{x}{4 x ^{2} + 3 x - 1}

y = - 0.75 x, (8, 0)

f (x) = e^{(3 - x)} + 7

\frac{x ^{2}}{1 - x ^{2}}

f (x) = - 5 x

What is the domain of 1/(sqrt(x^4-10x^2+9)) ?
The domain of 1/(sqrt(x^4-10x^2+9)) is x<-3\lor-1<x<1\lor x>3