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  4. Let A= x ∈ R: x is not a positive integer Define a function f :A → R as f(x) = (2x/x-1) then f is

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Q. Let $A=\{x \in R : x$ is not a positive integer} Define a function $f :A \to R$ as $f(x) = \frac{2x}{x-1}$ then $f$ is

JEE MainJEE Main 2019Relations and Functions - Part 2

Solution:

$f\left(x\right) = 2 \left(1+ \frac{1}{x-1}\right) $
$f'\left(x\right) = - \frac{2}{\left(x-1\right)^{2}} $
$ \Rightarrow f $ is one-one but not onto