Question:
Let $\mathrm{A}=\{x \in \mathbf{R}: x$ is not a positive integer $\}$. Define a function f: $\mathbf{A} \rightarrow \mathbf{R}$ as $f(x)=\frac{2 x}{x-1}$, then $f$ is:
Correct Option: , 4
Solution:
As $A=\{x \in R: x$ is not a positive integer $\}$
A function $f: A \rightarrow R$ given by $f(x)=\frac{2 x}{x-1}$
$f\left(x_{1}\right)=f\left(x_{2}\right) \Leftrightarrow x_{1}=x_{2}$
So, $f$ is one-one.
As $f(x) \neq 2$ for any $x \in A \Rightarrow f$ is not onto.
Hence $f$ is injective but not surjective.
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