When the graph of the function $y = \mathrm { f } ( x )$, defined on the real numbers, is reflected in the $y$-axis and then translated by 2 units in the negative $x$-direction, the result is the graph of the function $y = \mathrm { g } ( x )$. When the graph of the same function $y = \mathrm { f } ( x )$ is translated by 2 units in the negative $x$-direction and then reflected in the $y$-axis, the result is the graph of the function $y = \mathrm { h } ( x )$. Which one of the following conditions on $y = \mathrm { f } ( x )$ is necessary and sufficient for the functions $\mathrm { g } ( x )$ and $\mathrm { h } ( x )$ to be identical?
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When the graph of the function $y = \mathrm { f } ( x )$, defined on the real numbers, is reflected in the $y$-axis and then translated by 2 units in the negative $x$-direction, the result is the graph of the function $y = \mathrm { g } ( x )$.
When the graph of the same function $y = \mathrm { f } ( x )$ is translated by 2 units in the negative $x$-direction and then reflected in the $y$-axis, the result is the graph of the function $y = \mathrm { h } ( x )$.
Which one of the following conditions on $y = \mathrm { f } ( x )$ is necessary and sufficient for the functions $\mathrm { g } ( x )$ and $\mathrm { h } ( x )$ to be identical?