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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
9 months, 1 week ago