Question

Let $f\left(x\right)=\left[x\right]$, where $\left[x\right]$ denotes the greatest integer less than or equal to $x$. If $a=\sqrt{{2011}^2+2012}$, then the value of $f\left(a\right)$ is

• A. $2010$
• B. $2011$
• C. $2012$
• D. $2013$
• E. $2014$

Answer 1

The correct option is B $2011$

Given, $f\left(x\right)=\left[x\right]$
Also, $a=\sqrt{(2011{)}^2+2012}=\sqrt{4046133}$ $=2011.5$

Since $\left[x\right]$ denotes the greatest integer less than or equal to $x$
Therefore, $f\left(a\right)=\left[a\right]=\left[2011.5\right]=2011$