Question #297202

The coordinates of the image of 𝑃(𝑥, 𝑦) when 𝑦 = 𝑓(𝑥) is transformed to


𝑦 = 2 𝑓(𝑥 − 3) − 1 are 𝑃′


(2, 3). Find the original point (𝑥, 𝑦).


1
Expert's answer
2022-02-18T01:43:10-0500

Let the original point be P(𝑥,𝑦).P(𝑥, 𝑦).


f(x3):P1(x+3,y)f(x-3): P_1(x+3, y)

2f(x3):P2(x+3,2y)2f(x-3): P_2(x+3, 2y)

2f(x3)1:P1(x+3,2y1)2f(x-3)-1: P_1(x+3, 2y-1)

Then


x+3=2=>x=1x+3=2=>x=-1

2y1=3=>y=22y-1=3=>y=2

The original point is P(1,2).P(-1, 2).



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