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Function notation question

  1. Jul 27, 2013 #1
    I have seen over and over statements like:
    [tex]
    \begin{aligned}
    &f(x)~\text{is a function of}\dots \\
    &\text{Let}~f(x)~\text{be a function that}\dots.
    \end{aligned}
    [/tex]
    This is probably a dumb question, but am I justified in feeling annoyed at these statements? The annoyance stems from my understanding that the "function" is [itex] f [/itex], not [itex] f(x) [/itex], i.e., in the definition,
    [tex]
    f : x \mapsto f(x),
    [/tex]
    so while [itex] f [/itex] is the literal rule that assigns a value to the point [itex] x [/itex], [itex] f(x) [/itex] is that actual value. Or am I mistaken?
     
  2. jcsd
  3. Jul 27, 2013 #2

    WannabeNewton

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    Science Advisor

    You are not mistaken. It is just an abuse of terminology.
     
  4. Jul 27, 2013 #3
    Thanks for your answer. But what do people mean generally? Are they referring to the rule, or the variable value of the output of the rule?
     
  5. Jul 27, 2013 #4

    WannabeNewton

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    Science Advisor

    The general meaning is that ##f## is the function, not ##f(x)##; in ##f:X\rightarrow Y,x \mapsto f(x)##, where ##X,Y## are sets, ##f## is the function from ##X## into ##Y## and it sends the element ##x## of ##X## to the element ##f(x)## of ##Y##. People simply say things like "consider the function ##f(x)##" for shorthand.
     
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