Join Sarthaks eConnect Today - Largest Online Education Community!
0 votes
5 views
in Sets, Relations and Functions by (36.4k points)
closed by

Show that the function f: N → N: f(x) = x2 is one-one into.

1 Answer

+1 vote
by (20.3k points)
selected by
 
Best answer

Consider N as the set of all natural numbers

It is given that f: N → N: f(x) = x2 Ɐ x ∈ N

We know that

f(x1) = f(x2)

It can be written as

x12 = x22

So we get

x12 – x22 = 0

We get

(x1 – x2) (x1 + x2) = 0

Here, (x1 – x2) = 0 where x1 = x2

Hence, f is one-one.

Consider A = {1, 2, 3, 4} and B = {1, 4, 9, 16, 25}

Here, f: A → B: f(x) = x2

By substituting the values

f(1) = 12 = 1

f(2) = 22 = 4

f(3) = 32 = 9

f(4) = 42 = 16

Hence, every moment in A has unique image in B. Here, ∃ 25 ∈ B which has no pre-image in A f is into.

Related questions

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...