C3 transformation Q Watch

hi-zen-berg
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Describe a sequence of two geometrical transformations that maps the graph of y=f(x) onto y=f(2x-1)

AQA C3 JUN 13

i feel that (2x-1)= 2(x-0.5)
therefore translation through [0.5, 0]
then stretch sf 1/2 parallel to x axis

however markscheme disagrees with me

can someone please explain why im wrong? thanks very much
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B_9710
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Consider 2 separate transformations mapping f(x) to f(2x-1).
To get from f(x) to f(x-1) it is a translation through vector  \mathbf{i} . Let us set f(x-1)=g(x).
Now to get from f(x-1) to f(2x-1) or equivalently from g(x) to f(2x-1) we do g(2x) which is a stretch parallel to the x axis, SF 1/2.
You could do these in the opposite order but there's a difference.
If we start with f(x) again, to get to f(2x) this time (doing the stretch first) it is a stretch parallel to the x-axis SF 1/2. Let us define f(2x) to be g(x).
To get from f(2x) to f(2x-1) or equivalently from g(x) to f(2x-1) we apply g(x-1/2) as we are replacing x with x-1/2 we get  f(2(x-1/2))= f(2x-1) .
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