domain of function

[alyren]

what is the domain of the function f(x)= sqrt(x^3-2x^2)?

i got x>2, (2,infinite) is this right?

 

[galactus]

Close.

\(\displaystyle x\geq 2\)

\(\displaystyle [2, \;\ {\infty})\)

 

[BigGlenntheHeavy]

\(\displaystyle Given \ f(x) \ = \ \sqrt{x^3-2x^2}, \ find \ its \ domain.\)

\(\displaystyle x^3-2x^2 \ \ge \ 0, \ x^2(x-2) \ \ge \ 0, \ x \ = \ 0 \ or \ x \ \ge \ 2.\)

\(\displaystyle Ergo, \ domain \ = \ \{0\} \ U \ [2,\infty)\)

 

[lookagain]

[/tex]

\(\displaystyle x^3-2x^2 \ \ge \ 0, \ x^2(x-2) \ \ge \ 0, \ x \ = \ 0 \ and \ x \ \ge \ 2.\)

\(\displaystyle Ergo, \ domain \ = \ \{0\} \ U \ [2,\infty)\)

It's a union (as opposed to an intersection), so it is \(\displaystyle \ \ x = 0 \ \ OR \ \ x \ge 2.\)

Keep the same interval notation answer.