0
$\begingroup$

I understand intuition of the following formula and function composition, however could use guidance understanding formalisms on how the argument $(x)$ is distributed to $f$ below:

$f\colon X\to Y$ and $g\colon Y$ to Z and $h\colon Z\to W$

$x \in X$

$ h\circ(g\circ f)(x)=h(g\circ f(x))= h(g(f(x))=h\circ g(f(x))=(h\circ g)\circ f(x). $

Is there a rule or identity such that the ordered list of arguments $(x)$ is used as an argument to $f$?

ANSWER

The definition of $\circ$:

$$(F \circ G)(x) = F(G(x))$$

The first step $h \circ (g \circ f)(x) = h((g \circ f)(x))$ applies the definition by putting in $h$ for $F$, and $g \circ f$ for $G$

$\endgroup$
0
$\begingroup$

I'm not sure what you mean by "how the argument ($x$) is distributed to $f$ below". Each of the steps you show is simply applying the definition of $\circ$:

$$(F \circ G)(x) = F(G(x))$$

For example, the first step $h \circ (g \circ f)(x) = h((g \circ f)(x))$ applies the definition by putting in $h$ for $F$, and $g \circ f$ for $G$.

$\endgroup$
  • $\begingroup$ Definitions! Thanks! $\endgroup$ – Nick May 16 at 3:08

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.