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{SECT 0 {SECT 0 {PARA 0 "" 0 "" {TEXT 26 7 "Advice:" }{TEXT -1 20 "  D
efining functions" }}{PARA 0 "" 0 "" {TEXT -1 16 "                " }}
{PARA 0 "" 0 "" {TEXT -1 45 "Here is a correct way of defining a funct
ion:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "f:= x -> x^2 + 1;" }
}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"fG:6#%\"xG6\"6$%)operatorG%&arrow
GF(,&*$9$\"\"#\"\"\"F0F0F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 75 "You can \+
then evaluate such a function with a constant or variable argument:" }
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$%\"uG\"\"#\"\"\"F'F'" }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "f(3);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"#5" }}}
{PARA 0 "" 0 "" {TEXT -1 70 "Similarly, for a function of several vari
ables (note the parentheses):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "g:= (x,y) -> x+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gG:6$
%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&9$\"\"\"*$9%\"\"#F/F)F)" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(u,v);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&%\"uG\"\"\"*$%\"vG\"\"#F%" }}}{PARA 0 "" 0 "" {TEXT 
-1 78 "On the other hand, the following defines an expression rather t
han a function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "h:= x^2 +
 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*$%\"xG\"\"#\"\"\"F)F)
" }}}{PARA 0 "" 0 "" {TEXT -1 176 "This is no problem if that's what y
ou wanted, but functions and expressions are used in different ways.  \+
In particular, you get a strange-looking result if you try to evaluate
 " }{MPLTEXT 0 21 1 "h" }{TEXT -1 25 " as you would a function:" }}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(u);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&*$-%\"xG6#%\"uG\"\"#\"\"\"F*F*" }}}{PARA 0 "" 0 "" 
{TEXT -1 21 "In order to evaluate " }{MPLTEXT 0 21 1 "h" }{TEXT -1 19 
" for some value of " }{MPLTEXT 0 21 1 "x" }{TEXT -1 15 ", you must us
e " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 13 "subs(x=u, h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&
*$%\"uG\"\"#\"\"\"F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 62 "Since in ordin
ary mathematics we often speak of \"the function " }{XPPEDIT 18 0 "f(x
) = x^2 + 1" "/-%\"fG6#%\"xG,&*$F&\"\"#\"\"\"\"\"\"F*" }{TEXT -1 44 "
\", a common beginner's mistake is to define " }{MPLTEXT 0 21 4 "f(x)
" }{TEXT -1 21 " instead of defining " }{MPLTEXT 0 21 1 "f" }{TEXT -1 
1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 15 "F(x):= x^2 + 1;" }}
{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%\"FG6#%\"xG,&*$F'\"\"#\"\"\"F+F+" }
}}{PARA 0 "" 0 "" {TEXT -1 56 "Beware!  Everything seems fine, as long
 as you use only " }{MPLTEXT 0 21 4 "F(x)" }{TEXT -1 27 ".  But when y
ou try to use " }{MPLTEXT 0 21 1 "F" }{TEXT -1 54 " with some other ar
gument, it appears to be undefined:" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 5 "F(u);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%\"FG6#%\"uG
" }}}{PARA 0 "" 0 "" {TEXT -1 49 "This is not surprising, since in fac
t it is only " }{MPLTEXT 0 21 4 "F(x)" }{TEXT -1 10 ", and not " }
{MPLTEXT 0 21 1 "F" }{TEXT -1 43 " of anything else, that you have def
ined.  " }}{PARA 0 "" 0 "" {TEXT -1 93 "There is a legitimate use of s
uch a construction (it places a value in the remember table of " }
{MPLTEXT 0 21 1 "F" }{TEXT -1 4 ").  " }}}{SECT 0 {PARA 0 "" 0 "" 
{TEXT 26 9 "See also:" }{TEXT -1 1 " " }{HYPERLNK 17 "function" 2 "fun
ction" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "remember" 2 "remember" "" }
{TEXT -1 2 ", " }{HYPERLNK 17 "subs" 2 "subs" "" }}}{SECT 0 {PARA 0 "
" 0 "" {TEXT 26 23 "Maple Advisor Database " }{TEXT -1 16 " R. Israel,
 1997" }}}}{MARK "0 20 0" 6 }{VIEWOPTS 1 1 0 1 1 1803 }