  It is shown that the extensions of exactly-solvable quantum mechanical
problems connected with the replacement of ordinary derivatives by Dunkl ones
and with that of classical orthogonal polynomials by exceptional orthogonal
ones can be easily combined. For such a purpose, the example of the Dunkl
oscillator on the line is considered and three different types of
rationally-extended Dunkl oscillators are constructed. The corresponding
wavefunctions are expressed in terms of exceptional orthogonal generalized
Hermite polynomials, defined in terms of the three different types of
$X_m$-Laguerre exceptional orthogonal polynomials. Furthermore, the extended
Dunkl oscillator Hamiltonians are shown to be expressible in terms of some
extended Dunkl derivatives and some anharmonic oscillator potentials.
