Let A=\{x: x R, x is not a positive integer \}Define f: A arrow R as f(x)=2x/x-1, then f is

Correct Answer is : injective but not surjective.

neither injective nor surjective.

Correct Answer is : injective but not surjective.

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KCET 2021 Math Solved Paper

Question : 26 of 60

Marks: +1, -0

Let

A=\{x: x \in R, x

\}

f: A \rightarrow R

f(x)=\frac{2x}{x-1}

f

Solution:

Given function,

f(x)=\frac{2x}{x-1}

On differentiating w.r.t.

x

, we get

f'(x)=\frac{(x-1)(2-2 x(1-0)}{(x-1)^{2}}

=\frac{2x-2-2x}{(x-1)^{2}}=\frac{-2}{(x-1)^{2}} < 0

Function is strictly decreasing.

Function is injective

\frac{2x}{x-1}=y \Rightarrow 2x=yx-y

⇒

y=x(y-2)

Let

x=\frac{y}{y-2} \notin \pi

for

y=2

f

is not surjective.

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