Question

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

• A. $\pm \sqrt{(1-x^2)}$
• B. $\sqrt{(1-x^2)}$
• C. $-\sqrt{(1-x^2)}$
• D. $\sqrt{(1+x^2)}$

Answer 1

Answer: (B), (C)

The correct options are
B

$\sqrt{(1-x^2)}$

C

$-\sqrt{(1-x^2)}$

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

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

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

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

$f\left(x\right)$ is a function . So it can be either $\sqrt{1-x^2}\text{or}-\sqrt{1-x^2}$ at a time.

It can't be both of them at the same time .