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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#>%\"fGR6#%\"xG6\"6$%)operatorG%&arrow
GF(,&*$)9$\"\"#\"\"\"F1F1F1F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 75 "You
 can then evaluate such a function with a constant or variable argumen
t:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "f(u);" }}{PARA 11 "" 1 
"" {XPPMATH 20 "6#,&*$)%\"uG\"\"#\"\"\"F(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 var
iables (note the parentheses):" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 19 "g:= (x,y) -> x+y^2;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"gGR6$
%\"xG%\"yG6\"6$%)operatorG%&arrowGF),&9$\"\"\"*$)9%\"\"#F/F/F)F)F)" }}
}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "g(u,v);" }}{PARA 11 "" 1 "" 
{XPPMATH 20 "6#,&%\"uG\"\"\"*$)%\"vG\"\"#F%F%" }}}{PARA 0 "" 0 "" 
{TEXT -1 78 "On the other hand, the following defines an expression ra
ther than a function:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "h:=
 x^2 + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"hG,&*$)%#x|irG\"\"#\"
\"\"F*F*F*" }}}{PARA 0 "" 0 "" {TEXT -1 176 "This is no problem if tha
t's what you wanted, but functions and expressions are used in differe
nt ways.  In particular, you get a strange-looking result if you try t
o evaluate " }{MPLTEXT 0 21 1 "h" }{TEXT -1 25 " as you would a functi
on:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 5 "h(u);" }}{PARA 11 "" 
1 "" {XPPMATH 20 "6#,&*$)-%#x|irG6#%\"uG\"\"#\"\"\"F+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 use " }{MPLTEXT 0 21 4 "subs" }{TEXT -1 4 " or " }{MPLTEXT 
0 21 4 "eval" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 
13 "subs(x=u, h);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"uG\"\"#\"
\"\"F(F(F(" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "eval(h,x=u);
" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*$)%\"uG\"\"#\"\"\"F(F(F(" }}}
{PARA 0 "" 0 "" {TEXT -1 62 "Since in ordinary mathematics we often sp
eak of \"the function " }{XPPEDIT 18 0 "f(x) = x^2 + 1" "6#/-%\"fG6#%
\"xG,&*$F'\"\"#\"\"\"F+F+" }{TEXT -1 44 "\", a common beginner's mista
ke is to define " }{MPLTEXT 0 21 4 "f(x)" }{TEXT -1 21 " instead of de
fining " }{MPLTEXT 0 21 1 "f" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 15 "F(x):= x^2 + 1;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>-%\"FG6#%#x|irG,&*$)F'\"\"#\"\"\"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 you try to use " }
{MPLTEXT 0 21 1 "F" }{TEXT -1 54 " with some other argument, it appear
s 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 fact it is only " }
{MPLTEXT 0 21 4 "F(x)" }{TEXT -1 10 ", and not " }{MPLTEXT 0 21 1 "F" 
}{TEXT -1 136 " of anything else, that you have defined.  There is a l
egitimate use of such a construction (it places a value in the remembe
r 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 "functi
on" 2 "function" "" }{TEXT -1 2 ", " }{HYPERLNK 17 "remember" 2 "remem
ber" "" }{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 21 4" 41 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 
1 }{PAGENUMBERS 0 1 2 33 1 1 }