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Thread: form of functions f (x) and g (x)

  1. #1
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    form of functions f (x) and g (x)

    can you help me to find the set of functions f (x) and g (x) that satisfy the two following relations respectively

    f (x + c) = c + f (x)and
    g (x + c) = c + g ^ 2 (x)
    with c is a non-zero constant
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  2. #2
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    Re: form of functions f (x) and g (x)

    Let $\displaystyle h(x)= f(x)-x$ and show that $\displaystyle h(x+c)=h(x)$ for all $\displaystyle x$

    meaning $\displaystyle h$ is periodic of period $\displaystyle c$
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  3. #3
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    Re: form of functions f (x) and g (x)

    Quote Originally Posted by popovyoussef View Post
    can you help me to find the set of functions f (x) and g (x) that satisfy the two following relations respectively

    f (x + c) = c + f (x)and
    g (x + c) = c + g ^ 2 (x)
    with c is a non-zero constant
    Does $g^2(x)$ mean $g(g(x))$ or does it mean $(g(x))^2$?
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  4. #4
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    Re: form of functions f (x) and g (x)

    Thank you very much for your answer
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  5. #5
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    Re: form of functions f (x) and g (x)

    I thank you very much for your interest. it mean g(g(x))
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