Question

Let $f:A\to B$ be an onto function such that $f\left(x\right)=\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x-2+2\sqrt{x-3}}$, then set ${}^{\prime }{B}^{\prime }$ is

• A. $[-2,0]$
• B. $[0,2]$
• C. $[-3,0]$
• D. $[-1,0]$

Answer 1

The correct option is A $[-2,0]$

$f:A\to B$ then $B$ is range set.

$f\left(x\right)=\sqrt{x-2-2\sqrt{x-3}}-\sqrt{x-2+2\sqrt{x-3}}$

$⟹\sqrt{(\sqrt{x-3}-1{)}^2}-\sqrt{(\sqrt{x-3}+1{)}^2}$

$⟹\sqrt{x-3}-1-\sqrt{x-3}-1$

$⟹-2$

$\therefore B\in [-2,0]$