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Q.
If $f ( x )=\frac{ x }{\ln x }$ and $g ( x )=\frac{\ln x }{ x }$. Then identify the CORRECT statement
Relations and Functions - Part 2
Solution:
(A) $\frac{1}{ g ( x )}=\frac{1}{\ln n / x } ; f ( x )=\frac{ x }{\ln x } x >0, x \neq 1$ for both
(B) $\frac{1}{ f ( x )}=\frac{1}{ x / \ln x } ; g ( x )=\frac{\ln x }{ x } \Rightarrow \frac{1}{ f ( x )}$ is not defined at $x =1$ but $g (1)=0$
(C) $f(x) \cdot g(x)=\frac{x}{\ln x} \cdot \frac{\ln x}{x}=1 $ if $x>0, x \neq 1 \Rightarrow$ N. I.
(D) $\frac{1}{ f ( x ) \cdot g ( x )}=\frac{1}{\frac{ x }{\ln x } \cdot \frac{\ln x }{ x }}=1 $ only for $x >0$ and $\left.x \neq 1\right]$