If f: 1,2,3, 0, 1, 2, is defined by f(x) = array r x 2 , if x is even - x -1 2 , if x is…

If \(f:\{1,2,3, \ldots\} \rightarrow\langle 0, \pm 1, \pm 2, \ldots\}\) is defined by \(f(x)\) =  \[\left\{\begin{array}{r} \frac{\mathbf{x}}{2} \text {, if } \boldsymbol{x} \text { is even } \\ -\frac{\mathbf{x}-1}{2} \text {, if } \boldsymbol{x} \text { is odd } \end{array}\right.\] then the value of \(f^{-1}(100)\) is