We know, for a circle of radius 1 centred at the origin: $$ y^2 + x^2 = 1$$
Now when I saw the graph of the given equation- any x-value in within the domain has two images, but how can that be?
Since I've read that in a function any pre-image cannot have two images.
And now the above can be equivalently written as, $$y = \sqrt{1-x^2} $$ But now, surprisingly(for me), any x-value doesn't have two images!
But why is that?
Best Answer
Because there is also $$y=-\sqrt{1-x^2}.$$
The circle with equation $x^2+y^2=1$ it's not a graph of a function.
We can understand it by another algebraic way. $$\left(\frac{3}{5},\frac{4}{5}\right)$$ and $$\left(\frac{3}{5},-\frac{4}{5}\right)$$ placed on the graph and this is a contradiction with a definition of the function.