Question

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

• A. injective but not surjective
• B. surjective but not injective
• C. bijective
• D. neither injective nor suriective

Answer 1

Answer: (A)

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