Question

The domain of $f\left(x\right)=\sqrt{1-\sqrt{x^2-14x+49}}$ is

• A. $[7,8]$
• B. $[6,7]$
• C. $[6,8]$
• D. $[0,8]$

Answer 1

The correct option is C $[6,8]$

Given : $f\left(x\right)=\sqrt{1-\sqrt{x^2-14x+49}}$
$\Rightarrow f\left(x\right)=\sqrt{1-|x-7|}$
$f\left(x\right)$ is defined when
$1-|x-7|\ge 0\Rightarrow |x-7|\le 1\Rightarrow -1\le x-7\le 1\Rightarrow 6\le x\le 8$