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Time Invariance

I understand what time invariance means but there are a few catches that I'm completely confused about: Suppose we have \(y(t)=x(\alpha t-\beta)\) to test time invariance we shift the input then "plug" it into the output:\(x_1(t_1)=x(t-t_o)\); so this is when I become confused; when we plug \(x_1(t_1)\) into \(y(t)\) we get: \(x(\alpha t-t_o-\beta)\) instead of \(y(t)=x(\alpha (t-t_o) -\beta)\); I believe there is some underling math I am unaware of; but, what is it? Any sources?

Note by Charles White
1 week, 4 days ago

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