{"id":6976,"date":"2021-07-23T23:19:25","date_gmt":"2021-07-23T14:19:25","guid":{"rendered":"https:\/\/sasamath.com\/blog\/?page_id=6976"},"modified":"2026-09-27T16:44:27","modified_gmt":"2026-09-27T07:44:27","slug":"functions","status":"publish","type":"page","link":"https:\/\/sasamath.com\/blog\/invitation-to-calculus\/functions\/","title":{"rendered":"\ud568\uc218"},"content":{"rendered":"
\n

\uc774 \uae00\uc740 \u300e\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c\u300f 0\uc7a5 2\uc808\uc758 \ub0b4\uc6a9\uc785\ub2c8\ub2e4.  (\ubbf8\uc801\ubd84\ud559 \uccab\uac78\uc74c \ucc28\ub840 \ubcf4\uae30<\/a>)<\/span><\/p>\n<\/div>\n

\uc774 \uc808\uc5d0\uc11c\ub294 \ud568\uc218\uc640 \ud569\uc131\ud568\uc218, \uc77c\ub300\uc77c \ud568\uc218\uc640 \uc704\ub85c\uc758 \ud568\uc218, \uc5ed\ud568\uc218\uc758 \ub73b\uacfc \uae30\ubcf8 \uc131\uc9c8\uc744 \uc0b4\ud3b4\ubcf4\uc790.<\/p>\n

<\/p>\n

\ud568\uc218\uc640 \ud569\uc131\ud568\uc218<\/h2>\n

\\(S\\)\uc640 \\(T\\)\uac00 \uc9d1\ud569\uc774\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(f:S \\rightarrow T\\)\uac00 \ud568\uc218<\/span>(function)\ub77c \ud568\uc740 \\(S\\)\uc758 \uac01 \uc6d0\uc18c \\(s\\)\uc5d0 \\(T\\)\uc758 \uc6d0\uc18c \\(t\\)\ub97c \uc815\ud655\ud788 \ud558\ub098\uc529 \ub300\uc751\uc2dc\ud0a8 \uac83\uc774\ub2e4. \uc5ec\uae30\uc11c \\(s\\)\uc5d0 \ub300\uc751\ub41c \uc6d0\uc18c\ub97c \\(f\\)\uc5d0 \uc758\ud55c \\(s\\)\uc758 \ud568\uc22b\uac12\uc774\ub77c\uace0 \ubd80\ub974\uace0 \\(f(s)\\)\uc640 \uac19\uc774 \ub098\ud0c0\ub0b8\ub2e4. \ud568\uc218 \\(f:S \\rightarrow T\\)\ub97c \uac04\ub2e8\ud788 \\(f\\)\ub77c\uace0 \ub098\ud0c0\ub0b4\uae30\ub3c4 \ud55c\ub2e4. \uc9d1\ud569 \\(S\\)\ub97c \\(f\\)\uc758 \uc815\uc758\uc5ed<\/span>(domain)\uc774\ub77c\uace0 \ubd80\ub974\uace0, \uc9d1\ud569 \\(T\\)\ub97c \\(f\\)\uc758 \uacf5\uc5ed<\/span>(codomain)\uc774\ub77c\uace0 \ubd80\ub978\ub2e4.<\/p>\n

\ub450 \ud568\uc218 \\(f,g:S\\rightarrow T\\)\uc5d0 \ub300\ud558\uc5ec \\(S\\)\uc758 \ubaa8\ub4e0 \uc6d0\uc18c \\(s\\)\uc5d0\uc11c \\(f(s)=g(s)\\)\uc774\uba74 \\(f=g\\)\ub77c\uace0 \ud55c\ub2e4.<\/p>\n

\ud568\uc218 \\(f:S \\rightarrow T\\)\uc758 \uce58\uc5ed<\/span>(range, image)\uc744 \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.
\n\\[
\n\\operatorname{ran}(f)
\n=
\n\\operatorname{Im}(f)
\n=
\n\\left\\{ t\\in T \\,\\vert\\, \\exists s\\in S : t=f(s) \\right\\}.
\n\\]\n<\/p>\n

\\(f:S \\rightarrow T\\)\uc640 \\(g:T \\rightarrow U\\)\uac00 \ud568\uc218\uc77c \ub54c, \ud569\uc131\ud568\uc218<\/span>(composition) \\(g\\circ f:S\\rightarrow U\\)\ub97c
\n\\[
\n(g\\circ f)(s)=g(f(s))
\n\\quad\\text{for all }s\\in S
\n\\]
\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \ud568\uc218\ub85c \uc815\uc758\ud55c\ub2e4.<\/p>\n

\n

\uc815\ub9ac 0.2.1. (\ud568\uc218\uc758 \ud569\uc131\uc758 \uacb0\ud569 \uc131\uc9c8)<\/span><\/p>\n

\uc138 \ud568\uc218 \\(f:S\\rightarrow T,\\) \\(g:T\\rightarrow U,\\) \\(h:U\\rightarrow V\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uc774\ub54c \ub2e4\uc74c\uc774 \uc131\ub9bd\ud55c\ub2e4.
\n\\[
\nh\\circ(g\\circ f)=(h\\circ g)\\circ f.
\n\\]
\n\uc989 \uc138 \ud568\uc218\uc758 \ud569\uc131\uc774 \uc815\uc758\ub420 \ub54c, \uad04\ud638\ub97c \ubb36\ub294 \ubc29\ubc95\uc5d0 \uad00\uacc4\uc5c6\uc774 \uadf8 \uacb0\uacfc\ub294 \ub3d9\uc77c\ud55c \ud568\uc218\uc774\ub2e4.<\/p>\n<\/div>\n

\n

\uc99d\uba85.<\/p>\n

\\(s\\in S\\)\ub77c\uace0 \ud558\uc790. \ud569\uc131\ud568\uc218\uc758 \uc815\uc758\uc5d0 \uc758\ud558\uc5ec
\n\\[
\n\\begin{aligned}
\n\\bigl(h\\circ(g\\circ f)\\bigr)(s)
\n&=h\\bigl((g\\circ f)(s)\\bigr)\\\\
\n&=h(g(f(s)))
\n\\end{aligned}
\n\\]
\n\uc774\uace0
\n\\[
\n\\begin{aligned}
\n\\bigl((h\\circ g)\\circ f\\bigr)(s)
\n&=(h\\circ g)(f(s))\\\\
\n&=h(g(f(s))).
\n\\end{aligned}
\n\\]
\n\ub530\ub77c\uc11c \\(S\\)\uc758 \ubaa8\ub4e0 \\(s\\)\uc5d0\uc11c \ub450 \ud568\uc218\uc758 \ud568\uc22b\uac12\uc774 \uac19\uc73c\ubbc0\ub85c
\n\\[
\nh\\circ(g\\circ f)=(h\\circ g)\\circ f
\n\\]
\n\uc774\ub2e4. <\/span><\/p>\n<\/div>\n

<\/p>\n

\uc77c\ub300\uc77c \ud568\uc218\uc640 \uc704\ub85c\uc758 \ud568\uc218<\/h2>\n

\\(f:S\\rightarrow T\\)\uac00 \ud568\uc218\ub77c\uace0 \ud558\uc790. \uc774\ub54c \ub2e4\uc74c\uacfc \uac19\uc774 \uc815\uc758\ud55c\ub2e4.<\/p>\n