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 the function f(x) 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

The correct option is B $\sqrt{1-x^2}$

The distance between (0,0) and (x,f(x)) 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(x) is a function . So it can be either $\sqrt{1-x^2}or-\sqrt{1-x^2}$ at a time.

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