What is the domain of (sqrt(x+6)-x)/(x^3-3x^2) ?

The domain of (sqrt(x+6)-x)/(x^3-3x^2) is -6 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

domain of (sqrt(x+6)-x)/(x^3-3x^2)

domain

\frac{x + 6 - x}{x ^{3} - 3 x ^{2}}

- 6 \leq x < 0 or 0 < x < 3 or x > 3

Interval Notation

[- 6, 0) \cup (0, 3) \cup (3, \infty)

Solution steps

Find non-negative values for radicals:

x \geq - 6

Find undefined (singularity) points:

x = 0, x = 3

Combine real regions and undefined points for final function domain

- 6 \leq x < 0 or 0 < x < 3 or x > 3

What is the domain of (sqrt(x+6)-x)/(x^3-3x^2) ?
The domain of (sqrt(x+6)-x)/(x^3-3x^2) is -6<= x<0\lor 0<x<3\lor x>3