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Thread: How to solve: If f(x) is even fcn, find range of b. f(x)=[3.5+bsinx] where [] is gif

  1. #11
    Elite Member mmm4444bot's Avatar
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    Quote Originally Posted by Abhishekdas View Post
    becoz [3.5+bsinx] is not equal to f(x) = 3.5 + b * sin(x)
    You answered that f(x) is not even because [tex]\lfloor{f(x)}\rfloor \ne f(x)[/tex].

    It's true that f(x) is not even, but I don't think your reason why is valid.

    f(x) is not even because sin(x) is not even.



    Consider the following function g.

    g(x) = 3.5 + b*cos(x)

    This is an even function because cos(x) is an even function.

    If we let b = 1, for an example, here's the graph of [tex]g(x)[/tex] and [tex]\lfloor{g(x)}\rfloor[/tex].

    [tex]\lfloor{g(x)}\rfloor \ne g(x)[/tex], yet g(x) is even.
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    "English is the most ambiguous language in the world." ~ Yours Truly, 1969

  2. #12

    I don't get it

    Quote Originally Posted by Subhotosh Khan View Post
    Then do you not see that the only way f(x) can become an even function is when b = 0
    I don't get it. Isn't f(x)= [3.5+bsinx]. Kindly elaborate.

  3. #13
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    Quote Originally Posted by Abhishekdas View Post
    I don't get it. Isn't f(x)= [3.5+bsinx]. Kindly elaborate.
    Yes, that is the definition of f(x). That can't be questioned as it was given!

    YOU said that a function f(x) is defined to be an even function if f(x) = f(-x), yet you claimed, as mbot pointed out, that f(x) is not even because
    [f(x)] is not equal to f(x). Where did this definition come from????

    You want to verify whether or not f(x)=f(-x), that is whether or not [3.5+bsin(x)] = [3.5+bsin(-x)] . When is this true? Remember that your answer should depend on b
    Last edited by Jomo; 07-07-2017 at 02:00 AM.
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

  4. #14
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    Quote Originally Posted by Subhotosh Khan View Post
    Then do you not see that the only way f(x) can become an even function is when b = 0
    Hmmm, how about |b|< 1/2 ???????
    A mathematician is a blind man in a dark room looking for a black cat which isn’t there. - Charles R. Darwin

  5. #15
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    Quote Originally Posted by Jomo View Post
    Hmmm, how about |b|< 1/2 ???????
    You are correct for OP.

    However, I was trying to "nudge" OP in that direction by assuming a simpler function (removing GIF operation).
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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