# B Range of function

1. Jul 18, 2016

### SamitC

Hello,
This is a very basic question but bothering me on some exercises.
,
Then how is the range of y is ? What if x is 0, then we can have y = 1 or y = -1.
While doing some exercises I encountered this issue and can't match the answers.

2. Jul 18, 2016

### .Scott

For the most part, $\sqrt{x}$ indicates the positive square root value.

Since, in this case, y is a function, there is not the slightest ambiguity. Functions are only allowed to have one value for any one input. So $y=\sqrt{1-x^2}$ refers only to the positive root.

3. Jul 18, 2016

### Staff: Mentor

If you just write $y = \sqrt{1-x^2}$ then it is only the positive root. Otherwise you should write $y = ± \sqrt{1-x^2}$ to indicate that you consider both roots. And even this is a bit sloppy because it means $y \in \{ ± \sqrt{1-x^2} \}$. I normally write $y_{1,2} = ± \sqrt{1-x^2}$.

4. Jul 18, 2016

### SamitC

The function part made it clear. Thanks.

5. Jul 18, 2016

### Erland

But the range isn't $y\ge 0$. It's $0\le y\le 1$.