Question

If $f:\{1,2,3,...\}\to \{0,\pm 1,\pm 2,...\}$ is defined by
$y=f\left(x\right)=\{\begin{array}{c}\frac{x}{2}\text{if x is even}\\ -\frac{(x-1)}{2},\text{if x is odd}\end{array}$, then $f^{-1}\left(100\right)$ is

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

Answer 1

Answer: (D)

$200$

Since $100$ is even $f^{-1}\left(x\right)=2x$

Hence $f^{-1}\left(100\right)=200$