Let a function f:(0, ∞) arrow(0, ∞) be defined by f(x)=|1-(1)/(x)| . Then f is :

Correct answer: D. None of the above f:(0, ∞) arrow(0, ∞) f(x)=|1-(1)/(x)| is not a function f(1)=0 and 1 ∈ domain but 0 co-domain Hence, f(x) is not a function.

JEE Main 201911 JanuaryEvening Shift

Exam: JEE Main
Year: 2019
Date: 11 January
Shift: Evening Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2019 · 11 January · Evening Shift · Mathematics · Functions

Let a function f:(0, ∞) arrow(0, ∞) be defined by f(x)=|1-(1)/(x)|...

Let a function

f:(0, \infty) \rightarrow(0, \infty)

be defined by

f(x)=\left|1-\frac{1}{x}\right| .

Then

f

is :

Options

Anot injective but it is surjective
Binjective only
Cneither injective nor surjective
DNone of the above

Correct answer

D. None of the above

Step-by-step solution

f:(0, \infty) \rightarrow(0, \infty)

f(x)=\left|1-\frac{1}{x}\right|

is not a function

\because f(1)=0

and

1 \in

domain but

0 \notin

co-domain Hence,

f(x)

is not a function.

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