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

Question

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 (A) injective but not surjective (B) not injective (C) surjective but not injective (D) neither injective nor surjective

Tardigrade Admin · Accepted Answer

f(x) = 2 (1+ (1/x-1)) f'(x) = - (2/(x-1)2) ⇒ f is one-one but not onto

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

injective but not surjective

not injective

surjective but not injective

neither injective nor surjective

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

Q. Let A={x∈R:x is not a positive integer} Define a function f:A→R as f(x)=x−12x​ then f is