Ask Questions, Get Answers

Want to ask us a question? Click here
Browse Questions
0 votes

If $f:R\rightarrow R$ is defined as $f(x)=[x]^2+[x+1]-3$ where $[x]$ is greatest integer of $x$, then what type of function is $f$?

$\begin{array}{1 1} \text{many to one and onto function.} \\ \text{many to one and into function.} \\\text{one to one and into function.} \\\text{ bijection.} \end{array}$

Can you answer this question?

1 Answer

0 votes
  • $[x+n]=[x]+n\:\:if\:\:n\in Z$
Factorising the quadratic expression in $[x]$ we get
$\Rightarrow\:x\in[1,2)\:\:or\:\:x\in [-2,-1)$
$\Rightarrow\:f$ is not one to one but is many to one function.
Also since $f(x)=[x]^2+[x]-2$ and $[x]^2,\:[x]$ take only integer values,
$f(x)$ assumes only integer values.i.e., $f(x)\in Z$.
$\Rightarrow\:$ Range of $f$ is Z
But given that $f:R\rightarrow R$
$\Rightarrow\:f$ is not onto function, but is into function.
$\Rightarrow\:f$ is many to one into function.
answered May 28, 2013 by rvidyagovindarajan_1

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