Ask Questions, Get Answers

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

Let A=R-{3},B=R-{1}.Let $f \;:\;A \rightarrow B$ be defined by $f(x)=\Large{\frac{x-2}{x-3}}\normalsize \forall x \in A$.Then show that f is bijective.

Can you answer this question?

1 Answer

0 votes
  • A function$f :A \to B$ is bijective if it is one-one ie $f(x)=f(y)=>x=y \qquad x \in A$ and onto ie for every $y \in B$ then exists $x \in A$ such that $f(x)=y$
Given :Let $A=R-\{3\}\qquad B=R -\{1\}$
$f:A \to B \qquad f(x)=\frac{x-2}{x-3} \qquad x \in A$
Step1: Injective or One-One function:
Let $f(x)=f(y) \qquad x,y \neq 3$
Hence f is one -one
Step 2: Surjective or On-to function:
Let $y \in B$ such that $y \neq 1$
$ yx-x=3y-2$
$x=\frac {3y-2}{y-1}$
$ x \in A$ since $y \neq 1$
Hence there exists $x \in A$ for every $y \in B$ such that $f(x)=y$
f is onto
Solution:Hence f is bijective



answered Mar 4, 2013 by meena.p
edited Mar 27, 2013 by meena.p

Related questions

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