Question

Let $f\left(x\right)=\frac{\left[x\right]}{[x+2]}$. Find the domain of $f\left(x\right)$

• A. $xϵR,x$ is not an integer
• B. $(-\infty ,-2)\cup [-1,\infty )$
• C. $xϵR,x\ne 1$
• D. $(-\infty ,-1]$

Answer 1

The correct option is B $(-\infty ,-2)\cup [-1,\infty )$

As from the definition of $\left[x\right]$ we get,

$\left[x\right]=\{\begin{array}{ccc}.& & \\ .& & \\ -1& \text{for}& -1\le x<0\\ 0& \text{for}& 0\le x<1\\ 1& \text{for}& 1\le x<2\\ .& & \\ .& & \end{array}$.

Now the given function $f\left(x\right)$ will be defined for $[x+2]\ne 0$.

And this occurs of $x\in (-\infty ,-2)\cup [-1,\infty )$.

So option (B) is correct.