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Math Help - Operations on Functions

  1. #1
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    Operations on Functions

    I'm sure that these are very simple questions, but I cannot find anything about it in my book or online. Unfortunately, I can only find what is (f + g)(x) equal to (f(x) + g(x)) and things like that.

    a) Find g such that (f + g)(x) = f(x) + c
    I would assume that this is asking what is g(x) equal to which I think would be c? Is that what it is asking?

    No idea what its asking on these:
    b) Find f such that (f x g)(x) = g(x) + c
    c) Find g given that (fg)(x) = cf(x)
    d) Find f given that (f x g)(x) = cg(x)

    Help please!! Thank you
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  2. #2
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    Quote Originally Posted by Iyokan View Post
    I'm sure that these are very simple questions, but I cannot find anything about it in my book or online. Unfortunately, I can only find what is (f + g)(x) equal to (f(x) + g(x)) and things like that.

    a) Find g such that (f + g)(x) = f(x) + c
    I would assume that this is asking what is g(x) equal to which I think would be c? Is that what it is asking?

    No idea what its asking on these:
    b) Find f such that (f x g)(x) = g(x) + c
    c) Find g given that (fg)(x) = cf(x)
    d) Find f given that (f x g)(x) = cg(x)

    Help please!! Thank you
    The definition of (f+g)(x) is f(x) + g(x). Similarly by definition, (f x g)(x) = f(x)g(x).

    So in all these problems, if you fix 'x' then f(x) and g(x) are some real numbers. But you have been given an equation in terms of f(x) (known) and g(x) (unknown) (which are real numbers). Try to solve for g(x) in terms of f(x) and constants.
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