Question

The domain of $f\left(x\right)=\sqrt{2-lo{g}_3(x-1)}$ is

• A. $(2,12]$
• B. $(\infty ,10]$
• C. $(3,12]$
• D. $(1,10]$

Answer 1

The correct option is D $(1,10]$

$\sqrt{2-lo{g}_3(x-1)}$

$x-1>0$

$\Rightarrow x>1$ …………$\left(1\right)$

Also,

$2-lo{g}_3(x-1)\ge 0$

$lo{g}_3(x-1)\le 2$

$(x-1)\le 3^2$

$\Rightarrow x-1\le 9$

$x\le 10$ …………..$\left(2\right)$

Intersection of $\left(1\right)$ & $\left(2\right)$

$x\in (1,10]$.