On the Sequence of Transformations of a Function [closed]

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I have read the threads on the sequence of transformations of a function and my understanding is that if one changes the order of the transformations, the outcome will change. I tried to test it by working on some simple functions. My question is that according to this order, the outcome of the transformation $f(x-a)$ is different from that $f(-(a-x))$. In the case of $f(x-a)$, the function is shifted $a$ units (take $a>0$) to the right. And in $f(-(a-x))$, we have first the reflection in the line $x=a/2$ and then the reflection in the y-axis. Therefore, one is not allowed to do the math and consider the inputs in the functions to be the same. Is this right? When I used the Maple to compare the results, it was the same. I think Maple takes $-(a-x)=x-a$.

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