\documentclass{article}
\usepackage{xepersian}
\makeatletter
\newbox\@slashboxa
\newbox\@slashboxb
\newbox\@slashboxc
\newcount\@slashboxwd
\newcount\@slashboxht
\newdimen\@slashsepl
\newdimen\@slashsepr
\def\slashbox{%
  \def\@slashboxpicture##1{%
    \put(0,0){\line(##1,1){\@slashboxwd}}%
    \put(0,\@slashboxht){\makebox(0,0)[tl]{\box\@slashboxa}}%
    \put(\@slashboxwd,0){\makebox(0,0)[br]{\box\@slashboxb}}%
  }%
  \@slashbox
}%
\def\backslashbox{%
  \def\@slashboxpicture##1{%
    \put(0,\@slashboxht){\line(##1,-1){\@slashboxwd}}%
    \put(0,0){\makebox(0,0)[bl]{\box\@slashboxa}}%
    \put(\@slashboxwd,\@slashboxht){\makebox(0,0)[tr]{\box\@slashboxb}}%
  }%
  \@slashbox
}%
\def\@slashbox{\@ifnextchar [{\@@slashbox}{\@@slashbox[0pt]}}
\def\@@slashbox[#1]{\@ifnextchar [{\@@@slashbox[#1]}{\@@@slashbox[#1][c]}}
\def\@@@slashbox[#1][#2]#3#4{%
% #1: width, #2: suppression of \tabcolsep on `l', `r', or `lr' side
% #3: left item, #4: right item
  \@slashsepl=\tabcolsep
  \@slashsepr=\tabcolsep
    \@tfor\@tempa :=#2\do{\expandafter\let
        \csname @slashsep\@tempa\endcsname=\z@}%
  \setbox\@slashboxa=\hbox{\strut\hskip\tabcolsep\shortstack[l]{#3}}%
  \setbox\@slashboxb=\hbox{\shortstack[r]{#4}\hskip\tabcolsep\strut}%
  \setbox\@slashboxa=\hbox{\raise\dp\@slashboxa\box\@slashboxa}%
  \setbox\@slashboxb=\hbox{\raise\dp\@slashboxb\box\@slashboxb}%
  \setbox\@slashboxc=\hbox{%
    \@tempdima=\wd\@slashboxa
    \advance\@tempdima by \wd\@slashboxb
    \advance\@tempdima by \@slashsepl
    \advance\@tempdima by \@slashsepr
    \@tempdimb=#1\relax%
    \ifdim\@tempdimb>\@tempdima \@tempdima=\@tempdimb\fi%
    \@tempdimb=\ht\@slashboxa
    \advance\@tempdimb by \dp\@slashboxa
    \advance\@tempdimb by \ht\@slashboxb
    \advance\@tempdimb by \dp\@slashboxb
    \@tempcnta=\@tempdima
    \@tempcntb=\@tempdimb
    \advance\@tempcnta by \@tempcntb
    \advance\@tempcnta by -1
    \divide\@tempcnta by \@tempcntb
    \ifnum\@tempcnta>6 \@tempcnta=6
      \@tempdimb=0.166666666\@tempdima
    \else
      \ifnum\@tempcnta<1 \@tempcnta=1\fi
      \@tempdima=\@tempdimb
      \multiply\@tempdima by \@tempcnta
    \fi%
    \advance\@tempdima by -\@slashsepl
    \advance\@tempdima by -\@slashsepr
    \@slashboxwd=\@tempdima
    \@slashboxht=\@tempdimb
    \@tempcntb=\@slashsepl
    \setlength{\unitlength}{1sp}%
    \begin{picture}(\@slashboxwd,\@slashboxht)(\@tempcntb,0)
    \advance\@tempdima by \@slashsepl
    \advance\@tempdima by \@slashsepr
    \@slashboxwd=\@tempdima
    \@slashboxpicture{\@tempcnta}
    \end{picture}%
  }%
  $\vcenter{\box\@slashboxc}$%
}
\makeatother
\begin{document}
\begin{table}[h]
\centering
\begin{LTR}
\begin{tabular}{c|ccc|c}
\backslashbox{$y$}{$x$}&$-1$&$0$&$1$&$f(y)$\\ \hline
$0$&$0$&$\frac{1}{3}$&$0$&$\frac{1}{3}$\\
$1$&$\frac{1}{3}$&$0$&$\frac{1}{3}$&$\frac{2}{3}$\\ \hline
$f(x)$&$\frac{1}{3}$&$\frac{1}{3}$&$\frac{1}{3}$&$1$\\
\end{tabular}
\end{LTR}
\caption{یک جدول مجانی.}
\end{table}
\end{document}