Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
Home  >>  CBSE XII  >>  Math  >>  Relations and Functions
0 votes

State with reason whether following functions have inverse: (iii) \(h: \{2,3,4,5,\} \to \{7,9,11,13\}\) with \(h=\{(2,7),(3,9),(4,11),(5,13) \} \)

This is part of a multi-part question on Clay6 and is answered here separately.
Can you answer this question?

1 Answer

0 votes
  • To check if a function is invertible or not ,we see if the function is both one-one and onto.
  • A function $f: X \rightarrow Y$ where for every $x1, x2 \in X, f(x1) = f(x2) \Rightarrow x1 = x2$ is called a one-one or injective function.
  • A function$ f : X \rightarrow Y$ is said to be onto or surjective, if every element of Y is the image of some element of X under f, i.e., for every $y \in Y$, there exists an element x in X such that $f(x) = y$.
Given function h defined by $h:\{2,3,4,5\} \to \{7,9,11,12,13\}$
Step1: Checking for Injective or One-One function:
From the given definition of $h=\{(2,7),(3,9),(4,11)(5,13)\}$, we can see that it is one-one, as for every ${2,3,4,5} \in h,\;$ all have distinct images under $h$, i.e., $h(2) \neq h(3) \neq h(4) \neq h(5)$.
Therfore, the function is one-one. We need to now check further for onto.
Step2: Checking for Surjective or On-to:
From the given definition of $h=\{(2,7),(3,9),(4,11)(5,13)\}$, we can see that every element in $\{7,9,11,13\}$ then exists an element $\{2,3,4,5\}$ such that $ h(x)=y$ is onto.
$\rightarrow$ The pre image of 7 is 2 , the pre image of 9 is 3, the pre image of 11 is 4 and pre image of 13 is 5
Therfore, the function is onto as well as one-one and hence is invertible.
answered Feb 25, 2013 by meena.p
edited Mar 19, 2013 by balaji.thirumalai

Related questions

Ask Question
student study plans
JEE MAIN, CBSE, AIPMT Mobile and Tablet App
The ultimate mobile app to help you crack your examinations
Get the Android App