## DESCRIPTION
## Algebra
## ENDDESCRIPTION

## KEYWORDS('algebra','inverse functions','domain')
## Tagged by cmd6a 8/6/06

## DBsubject('Algebra')
## DBchapter('Functions')
## DBsection('Inverse Functions')
## Date('')
## Author('')
## Institution('SUNYSB')
## TitleText1('')
## EditionText1('')
## AuthorText1('')
## Section1('')
## Problem1('')

DOCUMENT();        # This should be the first executable line in the problem.

loadMacros(
"PG.pl",
"PGbasicmacros.pl",
"PGchoicemacros.pl",
"PGanswermacros.pl",
"PGauxiliaryFunctions.pl"
);

TEXT(&beginproblem);

$showPartialCorrectAnswers = 0;

$a1 = random(2,15,1);
$b1 = random(1,15,1);
$c1 = random(-15,15,1);

$funct = "$a1 - x";

TEXT(EV2(<<EOT));
Let \[ f: R \longrightarrow R, f(x) = $a1 - x  \]
$PAR
\( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
EOT
$ans = 1/$a1;
&ANS(function_cmp($funct));

##############################mec2##############################
#$a1 = random(2,15,1);
#$b1 = random(1,15,1);
#$c1 = random(-15,15,1);
#
#$funct = "1/x - $a1";
#
#TEXT(EV2(<<EOT));
#Let \[ f(x) = \frac { 1 } { x + $a1 }  \]
#$PAR
#\( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
#EOT
#
#&ANS(function_cmp($funct));
#
##############################mec3##############################
$a1 = random(2,15,1);
$b1 = random(1,15,1);
$c1 = random(-15,15,1);

$funct = "($a1 - x)^(1/2)";

TEXT(EV2(<<EOT));
Let \[ f: [0,\infty) \longrightarrow R, f(x) = $a1 - x^2 \]
$PAR
\( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
EOT

&ANS(function_cmp($funct));

##############################mec4##############################
$a1 = random(1,5,1);
$b1 = random(6,10,1);
$c1 = random(-10,-1);

$ans = ($b1*$c1 - $a1)/(1 - $c1);

TEXT(EV2(<<EOT));
Let \[ f: C \longrightarrow D, f(x) = \frac { x + $a1} { x + $b1 } \]
$PAR
f is bijective from C to D.
$PAR
\( f^{-1}( $c1 ) = \) \{ans_rule(20) \} $PAR
EOT

&ANS(std_num_cmp($ans));
##############################mec5##############################
$a1 = random(2,6,1);
$b1 = non_zero_random(-10,10,1);
$c1 = non_zero_random(-5,5,1);
$c2 = $c1 + 1;
$d1 = random($c2,10,1);

TEXT(EV2(<<EOT));
Let \[ f(x) = \frac { 1 } { $a1} x + $b1 , \quad $c1 \le x \le $d1 \]
$PAR
The domain of \( f^{-1}\) is the interval \( [A,B] \)
$PAR
where \( A = \) \{ans_rule(10) \}
and where \( B = \) \{ans_rule(10) \} $PAR
EOT

$ans1 = $c1/$a1 + $b1;
$ans2 = $d1/$a1 + $b1;

&ANS(std_num_cmp($ans1));
&ANS(std_num_cmp($ans2));

##############################mec6##############################
$a1 = random(2,5,1);
$b1 = random(1,5,1);
$c1 = random(2,5,1);

$x1 = $a1 + $c1;

TEXT(EV2(<<EOT));
Let \[ f: R \longrightarrow R, f(x) = $a1 + $b1 x + $c1 e^x \]

\( f^{-1}($x1) = \) \{ans_rule(10) \}
$PAR
EOT

&ANS(std_num_cmp(0));

##############################mec7##############################
$a1 = random(2,15,1);
$b1 = random(1,15,1);
$c1 = random(-15,15,1);

TEXT(EV2(<<EOT));
If \( f: R \longrightarrow R, f(x) = $a1 x - $b1 \), then $BR
\( f^{-1}(y) = \) \{ans_rule(20) \} $BR
\( f^{-1}( $c1 ) = \) \{ans_rule(20) \}
$PAR
EOT
$ans1="(y+$b1)/$a1";
$ans2 = ($c1+$b1)/$a1;
&ANS(function_cmp($ans1, "y"), std_num_cmp($ans2));

ENDDOCUMENT();        # This should be the last executable line in the problem.