Thread: f(x) = x^1/3

1. f(x) = x^1/3

ok so for this project I have to identify all this stuff for the function
$f(x) = x^{1/3}$

and a few things that I have to identify I don't know.

1) What are intervals of continuity?
2) Explain one-to-one

I have no idea what both those things are. Please explain for me so that I can understand.

Thanks!

2. Originally Posted by yoman360

1) What are intervals of continuity?

I think you are being asked to provide what interval fr x these function is continuous. As x can be any real number in this case then the interval for continuity would be $(-\infty ,\infty)$

Originally Posted by yoman360

2) Explain one-to-one
The term one to one means that there is only one x value for any y value (and vice versa) for the function in question.

3. yoman360, perhaps this graph may help you . . . .

4. Originally Posted by pacman
yoman360, perhaps this graph may help you . . . .
nice graph ... what function is it?

5. Originally Posted by pacman
yoman360, perhaps this graph may help you . . . .
The range set is not specified, so wouldn't you assume Reals? In that case, an odd root can take a negative radicand and still produce a value in the Reals.

6. here is the much better view, domain of x is -2 to +2