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{SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 10 "Calculus I" }}{PARA 256 "
" 0 "" {TEXT -1 28 "Lesson 18: Inverse Functions" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}}{EXCHG {PARA 0 "" 0 "" {TEXT 256 9 "Example 1" }
{TEXT -1 60 "\nFor each of the following functions, determine whether \+
the " }}{PARA 0 "" 0 "" {TEXT -1 58 "function is one-to-one. If yes, p
lot the function and its " }}{PARA 0 "" 0 "" {TEXT -1 26 "inverse on t
he same axes. " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "restart; \+
with(plots):" }}{PARA 7 "" 1 "" {TEXT -1 50 "Warning, the name changec
oords has been redefined\n" }}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 5 "1a) \+
 " }{XPPEDIT 18 0 "f(x) = 2*x + 1" "6#/-%\"fG6#%\"xG,&*&\"\"#\"\"\"F'F
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"f1:= x -> 2*x + 1; " }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6
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{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "g1:= x -> .5 * ( x - 1);" }
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" 0 "" {MPLTEXT 1 0 58 "a1:= plot(f1(x), x = -10..10, thickness=2, col
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0 "" {MPLTEXT 1 0 53 "c1:= plot(x, x = -10..10, thickness=2, color = b
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{MPLTEXT 1 0 58 "e1:= textplot([7,10,`y=x`], thickness=2, color = mage
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3,`g1`], thickness=2, color = magenta):" }}}{EXCHG {PARA 0 "> " 0 "" 
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l$\"3!)4c_Fjew7F17$F]al$\"3-&4Sv&QH>>F17$F`al$\"3CoO$\\!zpuDF17$Fcal$
\"3!4\"))*Q>JY?$F17$Ffal$\"3>l%fdLV4!QF17$Fial$\"3&[Dw?K#*[W%F17$F\\bl
$\"3\"*eoz8Ol/]F17$F_bl$\"3U?'z@Ws*zbF17$Fbbl$\"3Y(GhB%**>zgF17$Febl$
\"3!ogrtz[')f'F17$Fhbl$\"3U]!e4/]-1(F17$F[cl$\"3=L,8\")Qc7vF17$F^cl$\"
3>!)Qd?13BzF17$Facl$\"3G\"fd*>4R<$)F17$Fdcl$\"3))[j\\nn?h')F17$Fgcl$\"
3_3O')>Uyu*)F17$Fjcl$\"3o5rJQ=VY#*F17$F]dl$\"35a:'o4\"\\g%*F17$F`dl$\"
3qln3SE!Hm*F17$Fcdl$\"3MurX7gL/)*F17$Ffdl$\"3?l,yOjH8**F17$Fidl$\"3c3e
dk<rw**F17$F\\elFgz-F\\[l6&F^[lF*F*F*Fc[l-Fael6&7$Fdel$\"#9F)Q*arcsin(
x)FgelFhelFc[l-%+AXESLABELSG6%Q\"xFgelQ!6\"%(DEFAULTG-%%VIEWG6$;$!+Fjz
q:!\"*$\"+Fjzq:Fi`mFb`m" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 
45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve 4" "Curve 5" "Curve
 6" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 
258 9 "Example 3" }{TEXT -1 32 "\nPlot y = cos(x) for x in [ 0,  " }
{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 46 " ]. Also plot the inverse \+
function.           " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "t2:
= x -> cos(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t2G%$cosG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "it2:= x -> arccos(x);" }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$it2G%'arccosG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 56 "v1:= plot(t2(x), x = 0..Pi, \+
thickness=2, color = black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 
0 55 "v2:= plot(it2(x), x = -1..1, thickness=2, color = red):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 51 "v3:= plot(x, x = 0..Pi, thic
kness=2, color = blue):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 63 "
v4:= textplot([1.6,.6,`cos(x)`], thickness=2, color = magenta):" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "v5:= textplot([2,1.6,`y=x`],
 thickness=2, color = magenta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 
1 0 65 "v6:= textplot([.7,1.7,`arcos(x)`], thickness=2, color = magent
a):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "display(\{v1,v2,v3,v
4,v5,v6\});" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 
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[l7$Ff[lFf[l7$F[\\lF[\\l-F06&F2F6F6F3F7-F$6&7$F*$\"\"'F,Q'cos(x)F.F/F7
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AULTG-%%VIEWG6$;F]\\l$\"+aEfTJ!\"*F_`m" 1 2 0 1 10 0 2 9 1 4 2 
1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+
4" "Curve 5" "Curve 6" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT 259 9 "Example 4" }{TEXT -1 32 "\nPlot f(x) = ta
n(x) for x in ( -" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 4 "/2, " }
{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 47 " /2). Also plot the invers
e function.          " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 17 "t3
:= x -> tan(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#t3G%$tanG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "it3:= x -> arctan(x);" }
{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$it3G%'arctanG" }}}
{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 75 "w1:= plot(t3(x), x = -Pi/2 +
 0.1.. Pi/2 - 0.1, thickness=2, color = black):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 57 "w2:= plot(it3(x), x = -10..10, thickness=2, co
lor = red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "w3:= plot(x,
 x = -10..10, thickness=2, color = blue):" }}}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 67 "w4:= textplot([5.5,2.5,`arctan(x)`], thickness=2, c
olor = magenta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "w5:= te
xtplot([8.5,7,`y=x`], thickness=2, color = magenta):" }}}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 60 "w6:= textplot([3,8,`tan(x)`], thickness=2
, color = magenta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "disp
lay(\{w1,w2,w3,w4,w5,w6\});" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" 
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2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve \+
3" "Curve 4" "Curve 5" "Curve 6" }}}}{EXCHG {PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT 260 9 "Example 4" }{TEXT -1 31 "\nPlot f(
x) = csc(x) for x in (-" }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 15 "
 /2,0) and (0, " }{XPPEDIT 18 0 "Pi;" "6#%#PiG" }{TEXT -1 48 " /2) . A
lso plot the inverse function.          " }}}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 18 "t4:= x -> csc(x); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6
#>%#t4G%$cscG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "it4:= x ->
 arccsc(x);" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$it4G%
'arccscG" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 65 "z1:= plot(csc(x
), x = -Pi/2 ..- 0.1, thickness=2, color = black):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 61 "z2:= plot(csc(x), x = 0.1..Pi/2, thickness=
2, color = black):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 55 "z3:= \+
plot(it4(x), x = 1..10, thickness=2, color = red):" }}}{EXCHG {PARA 0 
"> " 0 "" {MPLTEXT 1 0 57 "z4:= plot(it4(x), x = -10..-1, thickness=2,
 color = red):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 52 "z5:= plot
(x, x= -10..10, thickness=2, color = blue):" }}}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 62 "z6:= textplot([1.8,5,`csc(x)`], thickness=2, color
 = magenta):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 57 "z7:= textpl
ot([5,4,`y=x`], thickness=2, color = magenta):" }}}{EXCHG {PARA 0 "> \+
" 0 "" {MPLTEXT 1 0 65 "z8:= textplot([-6,-2,`arccsc(x)`], thickness=2
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lay(\{z1,z2,z3,z4,z5,z6,z7,z8\});" }{TEXT -1 0 "" }}{PARA 13 "" 1 "" 
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