TMUA 2019 Paper 2 Question 20

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