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How is the high school math function y=f( 1-x) transformed from y=fx and how is it symmetrical with y=f(x- 1)?
Make an image of y=fx about the y axis to get f(-x), and then translate the obtained function to the right by one unit to get y=f( 1-x).

These two functions are symmetric about x=0.5.

In order to clarify the independent variable, suppose that the independent variable of the function y=f( 1-x) is x 1 and the independent variable of y=fx is x2, then 1-x 1=x2 is (x 1+x2)/2=0.5.