Ask Questions, Get Answers

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

Which of the following functions from Z into Z are bijections?\begin{array}{1 1}(A)\;f(x)=x^3 & (B)\;f(x)=x+2\\(C)\;f(x)=2x+1 & (D)\;f(x)=x^2+1\end{array}

Can you answer this question?

1 Answer

0 votes
  • A function $f: Z \to Z$ is bijective if f is both one -one and onto
  • ie $f(x)=f(y) =>x =y$
  • and for every $y \in R$ then exists $ x\in R $ such that $f(x)=y$
$f(x)=x^3 \qquad x \in z$
$x_1 =x_2$
f is one one
But for $y=-2$ then does not exists $x \in Z$ such that $f(x)=-2$ ie $x^3=-2$
f is not onto
f is not bijection
$=> x_1+2=x_2+2$
f is one one
Also $y=x+2 \qquad \in z$ then there exists
$x=y-2 \qquad \in z$ such that
f is onto
Hence f=x+2 is bijection
'B' option is correct



answered Mar 5, 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