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Math Help - Exponential help

  1. #1
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    Exponential help

    Hi, I really need help on this problem.

    Let f(x) = (1/2)([a^x] + [a^-x]) if a> 0. Show that

    f(x + y) + f(x-y) = 2f(x)f(y)

    I really appreciated any help
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by BrianW View Post
    Hi, I really need help on this problem.

    Let f(x) = (1/2)([a^x] + [a^-x]) if a> 0. Show that

    f(x + y) + f(x-y) = 2f(x)f(y)

    I really appreciated any help
    f(x+y) = (1/2) (a^{x+y} + a^{-(x+y)})

    f(x+y) = (1/2) (a^{x-y} + a^{-(x-y)})

    so:

    f(x+y) + f(x-y) = (1/2) [a^{x+y} + a^{-(x+y)} + a^{x-y} + a^{-(x-y)}]

    ........ = (1/2) [ a^x (a^y-a^{-y}) + a^{-x} (a^y-a^{-y})]

    ........ = f(y) [ a^x + a^{-x}] = 2 f(y) f(x) = 2 f(x) f(y)

    RonL
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