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

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

KCETKCET 2021Relations and Functions - Part 2

Solution:

$f'(x)=\frac{-2}{(x-1)^{2}}<0$
$f$ is s.d. $f$ is one-one
$\frac{2 x}{x-1}=y$
$\Rightarrow x=\frac{y}{y-2} \notin \pi$
for $y=2f$ is not out