Question

Let f(x) be a function defined on [-1, 1]. If the distance between (0,0) and (x, f(x)) is 1 unit, then find the function.

Answer 1

The distance between $(0,0)$ and $(x,f(x\left)\right)$ is 1 unit

$\Rightarrow$ $\sqrt{x^2+f(x{)}^2}=1$

$f(x{)}^2=1-x^2$

$f\left(x\right)=\pm \sqrt{1-x^2}$

$\left(f\right(x\left)\right)$ can not be either $\sqrt{1-x^2}or-\sqrt{1-x^2}$.

Therefore f(x) is not a function.