They all are same!

Algebra Level 4

If

f ( x ) = x l n ( x ) \displaystyle f(x) = \frac{x}{ln(x)}

And

g ( x ) = l n ( x ) x \displaystyle g(x) = \frac{ln(x)}{x}

Then identify the correct statement

1 f ( x ) . g ( x ) = 1 x > 0 \frac{1}{f(x).g(x)}= 1 \quad\forall \quad x > 0 f ( x ) . g ( x ) = 1 x > 0 f(x).g(x) = 1 \quad\forall \quad x > 0 1 f ( x ) \frac{1}{f(x)} and g ( x ) g(x) are identical functions 1 g ( x ) \frac{1}{g(x)} and f ( x ) f(x) are identical functions

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