View of /trunk/NationalProblemLibrary/SUNYSB/WebWorkInverse.pg

    1 ## DESCRIPTION
    2 ## Algebra
    3 ## ENDDESCRIPTION
    4 
    5 ## KEYWORDS('algebra','inverse functions','domain')
    6 ## Tagged by cmd6a 8/6/06
    7 
    8 ## DBsubject('Algebra')
    9 ## DBchapter('Functions')
   10 ## DBsection('Inverse Functions')
   11 ## Date('')
   12 ## Author('')
   13 ## Institution('SUNYSB')
   14 ## TitleText1('')
   15 ## EditionText1('')
   16 ## AuthorText1('')
   17 ## Section1('')
   18 ## Problem1('')
   19 
   20 DOCUMENT();        # This should be the first executable line in the problem.
   21 
   22 loadMacros(
   23 "PG.pl",
   24 "PGbasicmacros.pl",
   25 "PGchoicemacros.pl",
   26 "PGanswermacros.pl",
   27 "PGauxiliaryFunctions.pl"
   28 );
   29 
   30 TEXT(&beginproblem);
   31 
   32 $showPartialCorrectAnswers = 0;
   33 
   34 $a1 = random(2,15,1);
   35 $b1 = random(1,15,1);
   36 $c1 = random(-15,15,1);
   37 
   38 $funct = "$a1 - x";
   39 
   40 TEXT(EV2(<<EOT));
   41 Let \[ f: R \longrightarrow R, f(x) = $a1 - x  \]
   42 $PAR
   43 \( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
   44 EOT
   45 $ans = 1/$a1;
   46 &ANS(function_cmp($funct));
   47 
   48 ##############################mec2##############################
   49 #$a1 = random(2,15,1);
   50 #$b1 = random(1,15,1);
   51 #$c1 = random(-15,15,1);
   52 #
   53 #$funct = "1/x - $a1";
   54 #
   55 #TEXT(EV2(<<EOT));
   56 #Let \[ f(x) = \frac { 1 } { x + $a1 }  \]
   57 #$PAR
   58 #\( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
   59 #EOT
   60 #
   61 #&ANS(function_cmp($funct));
   62 #
   63 ##############################mec3##############################
   64 $a1 = random(2,15,1);
   65 $b1 = random(1,15,1);
   66 $c1 = random(-15,15,1);
   67 
   68 $funct = "($a1 - x)^(1/2)";
   69 
   70 TEXT(EV2(<<EOT));
   71 Let \[ f: [0,\infty) \longrightarrow R, f(x) = $a1 - x^2 \]
   72 $PAR
   73 \( f^{-1}( x ) = \) \{ans_rule(20) \} $PAR
   74 EOT
   75 
   76 &ANS(function_cmp($funct));
   77 
   78 ##############################mec4##############################
   79 $a1 = random(1,5,1);
   80 $b1 = random(6,10,1);
   81 $c1 = random(-10,-1);
   82 
   83 $ans = ($b1*$c1 - $a1)/(1 - $c1);
   84 
   85 TEXT(EV2(<<EOT));
   86 Let \[ f: C \longrightarrow D, f(x) = \frac { x + $a1} { x + $b1 } \]
   87 $PAR
   88 f is bijective from C to D.
   89 $PAR
   90 \( f^{-1}( $c1 ) = \) \{ans_rule(20) \} $PAR
   91 EOT
   92 
   93 &ANS(std_num_cmp($ans));
   94 ##############################mec5##############################
   95 $a1 = random(2,6,1);
   96 $b1 = non_zero_random(-10,10,1);
   97 $c1 = non_zero_random(-5,5,1);
   98 $c2 = $c1 + 1;
   99 $d1 = random($c2,10,1);
  100 
  101 TEXT(EV2(<<EOT));
  102 Let \[ f(x) = \frac { 1 } { $a1} x + $b1 , \quad $c1 \le x \le $d1 \]
  103 $PAR
  104 The domain of \( f^{-1}\) is the interval \( [A,B] \)
  105 $PAR
  106 where \( A = \) \{ans_rule(10) \}
  107 and where \( B = \) \{ans_rule(10) \} $PAR
  108 EOT
  109 
  110 $ans1 = $c1/$a1 + $b1;
  111 $ans2 = $d1/$a1 + $b1;
  112 
  113 &ANS(std_num_cmp($ans1));
  114 &ANS(std_num_cmp($ans2));
  115 
  116 ##############################mec6##############################
  117 $a1 = random(2,5,1);
  118 $b1 = random(1,5,1);
  119 $c1 = random(2,5,1);
  120 
  121 $x1 = $a1 + $c1;
  122 
  123 TEXT(EV2(<<EOT));
  124 Let \[ f: R \longrightarrow R, f(x) = $a1 + $b1 x + $c1 e^x \]
  125 
  126 \( f^{-1}($x1) = \) \{ans_rule(10) \}
  127 $PAR
  128 EOT
  129 
  130 &ANS(std_num_cmp(0));
  131 
  132 ##############################mec7##############################
  133 $a1 = random(2,15,1);
  134 $b1 = random(1,15,1);
  135 $c1 = random(-15,15,1);
  136 
  137 TEXT(EV2(<<EOT));
  138 If \( f: R \longrightarrow R, f(x) = $a1 x - $b1 \), then $BR
  139 \( f^{-1}(y) = \) \{ans_rule(20) \} $BR
  140 \( f^{-1}( $c1 ) = \) \{ans_rule(20) \}
  141 $PAR
  142 EOT
  143 $ans1="(y+$b1)/$a1";
  144 $ans2 = ($c1+$b1)/$a1;
  145 &ANS(function_cmp($ans1, "y"), std_num_cmp($ans2));
  146 
  147 ENDDOCUMENT();        # This should be the last executable line in the problem.