$8\mathrm{.}2-2$ Recall that the autocorrelation function of a stationary process must satisfy $R_x^{**}()=R_x(-).$ Determine which of the following functions can be a valid autocorrelation function of a stationary random process.

$($a$)({}^2+9{)}^{-1}$

$($d$)N()+({}^2+4{)}^{-1}$

$($b$)({}^2-1{)}^{-1}$

$($e$)sin({}_0)$

$($c$)e^{-}u()$

$($f$)cos({}_0)$