Question

Assertion (A) : Let $f:(e,\infty )\to R$ defined by $f(x)=log(log(logx))$ is invertible.
Reason (R) : $f$ is both one-one & onto.

• A. Both (A) & (R) are individually true & (R) is correct 3. explanation of (A).
• B. Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).
• C. (A) is true but (R) is false.
• D. (A) is false but (R) is true.

Answer 1

Answer: (A)

As $x\in (e,\infty )$
$\Rightarrow logx>1$
$\Rightarrow log(logx)>log1$
$\Rightarrow log(logx)>0$
$\Rightarrow log(log(logx))>log0$
$\Rightarrow log(log(logx))\in (-\infty ,\infty )$
$\Rightarrow$ codomain of $f(x)=$ Range of $f(x)$
$\Rightarrow f$ is onto
Again log function is always $1-1$
$\therefore f(x)$ is both one - one & onto.