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Let the function $f$ take values $f(x,y,z)$. Define a function $g$ taking values $g(x,y)=f(x,y,x+y)$.

Is there a name for creating functions such as $g$, whose values are given only by the values of $f$? Can I say that $g$ is induced by $f$?

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  • $\begingroup$ There aren’t enough names for all methods of specifying a function. When choosing a name, you need to make sure that it is not occupied $\endgroup$
    – Minz
    Feb 2, 2020 at 11:28
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    $\begingroup$ @AlvinLepik: What sort of trouble are you thinking of? The expression is well-defined as long as $f$ has an appropriate domain. $\endgroup$
    – joriki
    Feb 2, 2020 at 12:13

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$g$ is the "composition" of $f$ with $h$ where $h(x,y)=(x,y,x+y)$. With $h$ defined, we could write $g=f\circ h$.

Sometimes, we might say that $g$ "factors through" $f$, but that phrase is a little ambiguous (see this answer for a list of ways that sort of phrasing is used).

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