Question

If $f:\{1,2,3,.....\}\to \{0,\pm 1,\pm 2,.....\}$ is defined by $f\left(n\right)=\{\begin{array}{cc}\frac{n}{2}& \text{if}niseven\\ -\left(\frac{n-1}{2}\right)& \text{if}nisodd\end{array}$ then $f^{-1}(-100)$ is

• A. Function is not invertible.
• B. $199$
• C. $201$
• D. $200$

Answer 1

The correct option is C $201$

$f\left(n\right)$ is positive if $n$ is even & negative if $n$ is odd.
$\therefore f^{-1}(-100)=-2x+1$
$=-2(-100)+1$
$=200+1$
$=201$