What is the domain of f(x)=sqrt((x(x^2-9))/(x^2-4)) ?

The domain of f(x)=sqrt((x(x^2-9))/(x^2-4)) is -3 = 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

domain of f(x)=sqrt((x(x^2-9))/(x^2-4))

domain

f (x) = \frac{x ( x ^{2} - 9 )}{x ^{2} - 4}

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

Interval Notation

[- 3, - 2) \cup [0, 2) \cup [3, \infty)

Solution steps

Find non-negative values for radicals:

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

Find undefined (singularity) points:

x = 2, x = - 2

Combine real regions and undefined points for final function domain

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

What is the domain of f(x)=sqrt((x(x^2-9))/(x^2-4)) ?
The domain of f(x)=sqrt((x(x^2-9))/(x^2-4)) is -3<= x<-2\lor 0<= x<2\lor x>= 3