# inverse hyperbolisch
checkfile=exos/checkfile1.proc
n=$counter
!if $level=0
    R=$counter
!else
    R=$level
!endif
var1=0
questiontype=0
plot=0
draw=0
math=1
arglist=f^-1(x),y
helptext=!record 42 of lang/remarks.$taal
question$n=!record 40 of lang/remarks.$taal
!if $R=1
    a=!randitem 1,2,3,4,5,6,7,8,9,10
    keuze=!randitem 0,1
    min=$[-1*(abs($a))-10]
    max=$[abs($a)+10]
    range=[$min:$max] [$min:$max]
    !if $keuze=1
	formula$n=f(x) \, =  \,$a + \frac{1}{x}
	var2=$a + 1/x
	answer$n=1/(x - $a)
	texanswer$n= y=$a + \frac{1}{x} \rightarrow \left[ \begin{array}{l} x_{inv}=$a + \frac{1}{y_{inv}} \\ \frac{1}{y_{inv}} \,=\,  x_{inv} - $a \\ y_{inv}=\frac{1}{x_{inv} - $a} \\  f^{-1}(x)=\frac{1}{x - $a}  \end{array}
    !else
	formula$n=f(x) \, =  \,$a - \frac{1}{x}
	var2=$a - 1/x
	answer$n=1/($a - x)
	texanswer$n= y=$a - \frac{1}{x} \rightarrow \left[ \begin{array}{l} x_{inv}=$a - \frac{1}{y_{inv}} \\ \frac{1}{y_{inv}} \,=\, $a -  x_{inv} \\ y_{inv}=\frac{1}{$a - x_{inv}} \\  f^{-1}(x)=\frac{1}{$a - x}  \end{array}
    !endif
!endif

!if $R=2
    a=!randitem 1,2,3,4,5,6,7,8,9,10
    b=!randitem -1,1
    pm=!randitem -,+
    !if $pm=+
	mp=-
    !else
	mp=+
    !endif
    min=$[-1*(abs($a))-10]
    max=$[abs($a)+10]
    range=[$min:$max] [$min:$max]
    formula$n=f(x) \, = \, \frac{$b}{x $pm $a}
    answer$n=$b/(x) $mp $a
    texanswer$n= y = \frac{$b}{x $pm $a} \rightarrow \left[ \begin{array}{l} x_{inv}= \frac{$b}{y_{inv} $pm $a} \\ x_{inv}\left( y_{inv} $pm $a \right) = $b \\ y_{inv} $pm  $a = \frac{$b}{x}  \\ y_{inv}= \frac{$b}{x} $mp $a   \\ f^{-1}(x) = \frac{$b}{x} $mp $a \end{array}
    var2=$b/(x $pm $a)
!endif

!if $R>2
    a=!randitem 1,2,3,4,5,6,7,8,9,10
    b=!randitem -2,-3,-4,-5,2,3,4,5
    pm=!randitem -,+
    !if $pm=+
	mp=-
    !else
	mp=+
    !endif
    min=$[-1*(abs($a))-10]
    max=$[abs($a)+10]
    range=[$min:$max] [$min:$max]
    formula$n=f(x) \, = \, \frac{$b}{x $pm $a}
    answer$n=$b/(x) $mp $a
    texanswer$n= y = \frac{$b}{x $pm $a} \rightarrow \left[ \begin{array}{l} x_{inv}= \frac{$b}{y_{inv} $pm $a} \\ x_{inv}\left( y_{inv} $pm $a \right) = $b \\ y_{inv} $pm  $a = \frac{$b}{x}  \\ y_{inv}= \frac{$b}{x} $mp $a   \\ f^{-1}(x)= \frac{$b}{x} $mp $a  \end{array}
    var2=$b/(x $pm $a)
!endif

!if $teaching=1
    exotext=!record 41 of lang/remarks.$taal
    insplot_set=size 0.6,0.6 ;grid ;xlabel "<x-axis>";ylabel"<y-axis>" ;border 
    !insplot $range $var2 notitle, $(answer$n) notitle, x 
    exotext=<a onmouseover="return escape('<img src=$wims_ref_name?&session=$session&module=$module&cmd=getins&special_parm=insert-1.gif>')">$exotext
!else
    exotext=$empty
!endif
