What is the domain of f(x)= 1/(sqrt(x^4-65x^2+64)) ?

The domain of f(x)= 1/(sqrt(x^4-65x^2+64)) is x 8

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domain of f(x)= 1/(sqrt(x^4-65x^2+64))

domain

f (x) = \frac{1}{x ^{4} - 65 x ^{2} + 64}

x < - 8 or - 1 < x < 1 or x > 8

Interval Notation

(- \infty, - 8) \cup (- 1, 1) \cup (8, \infty)

Solution steps

Find non-negative values for radicals:

x \leq - 8 or - 1 \leq x \leq 1 or x \geq 8

Find undefined (singularity) points:

x = 8, x = - 8, x = 1, x = - 1

Combine real regions and undefined points for final function domain

x < - 8 or - 1 < x < 1 or x > 8

f (x) = - x - 14

f (x) = x^{4} - 2 x^{2} + 7

y = 4 x^{2} - 4 x + 1

x^{3} - 4 x^{2} - 3 x + 8

(- 1, - 3), (1, 1)

What is the domain of f(x)= 1/(sqrt(x^4-65x^2+64)) ?
The domain of f(x)= 1/(sqrt(x^4-65x^2+64)) is x<-8\lor-1<x<1\lor x>8