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Math Help - algebra of functions

  1. #1
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    Post algebra of functions

    Consider the function y(t) = x(t)*x(t-1). I am trying to prove that this function is linear. I was trying to use the relationship (fg)(x) = f(x) * g(x), but I can't figure out how to go backwards with y(t), to get (fg)(x). I'm not even sure you can since you have a "t" in one function and a "t-1" in the other function. As an FYI, to prove linearity you have to show that x1(t)x1(t-1) + x2(t)x2(t-1) = y1(t) + y2(t). Please be specific with your answer; it would help a lot.

    thanks
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  2. #2
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by afried01 View Post
    Consider the function y(t) = x(t)*x(t-1). I am trying to prove that this function is linear. I was trying to use the relationship (fg)(x) = f(x) * g(x), but I can't figure out how to go backwards with y(t), to get (fg)(x). I'm not even sure you can since you have a "t" in one function and a "t-1" in the other function. As an FYI, to prove linearity you have to show that x1(t)x1(t-1) + x2(t)x2(t-1) = y1(t) + y2(t). Please be specific with your answer; it would help a lot.

    thanks

    function is linear if shifted input produce shifted output
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  3. #3
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    reply to first answer

    This is a bit beyond me. Can you use basic function relationships to prove this, i.e., something within pre-calculus math? Or at least explain that relationship above in more detail.

    thanks
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  4. #4
    Senior Member yeKciM's Avatar
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    sorry about that ...

    x(t) and x(t-1) is the same function, just x(t-1) is shifted to the left

    (i'll try to remember way that i can explain to you more properly .... sorry again for that bad reply )
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  5. #5
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    reply to second answer

    How can you use the relationship (fg)(x) = f(x) * g(x)? In other words how can I get from x(t)*x(t-1) to (fg)(x)?

    Thanks
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