Question

Let $f:A\to b$ be a function defined by f(x) =$\sqrt{1-x^2}$

• A. f(x) is one-one if A =[0,1]
• B. f(x) is onto if B = [0,1]
• C. f(x) is one-one if A =[-1 , 0]
• D. f(x) is onto if B = [-1,1]

Answer 1

Answer: (A)

f(x) is one-one if A =[0,1]

$f:A\to B$

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

When $x=0$

$f\left(0\right)=\sqrt{1-0}$

$=1$

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

$=0$

$f\left(x\right)$ is one - one function when $A=[0,1]$