document.write( "Question 941055: The function f:x->px+q, xER, is such that f^-1 (6)=3 and f^-1 (29)=-2. \r
\n" ); document.write( "\n" ); document.write( "Find f^-1 (27).\r
\n" ); document.write( "\n" ); document.write( "I have spent a long time trying to figure this out and I can't get it.
\n" ); document.write( "The answer given in the textbook is 6.
\n" ); document.write( "I have found the inverse function to be f^(-1): 1/p (x-q) so I am guessing that means I subtract or add something to x and then divide it.
\n" ); document.write( "Any help on this would be greatly appreciated. \r
\n" ); document.write( "\n" ); document.write( "Thanks \n" ); document.write( "

Algebra.Com's Answer #573601 by Fombitz(32388) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"f%5E%28-1%29%286%29=3\"$ so $\"f%283%29=6\"$
\n" ); document.write( " $\"f%5E%28-1%29%2829%29=-2\"$ so $\"f%28-2%29=29\"$
\n" ); document.write( " $\"f%28x%29=px%2Bq\"$
\n" ); document.write( "1. $\"f%283%29=3p%2Bq=6\"$
\n" ); document.write( "2. $\"f%28-2%29=-2p%2Bq=29\"$
\n" ); document.write( "Subtract eq. 1 from eq. 2,
\n" ); document.write( " $\"-2p%2Bq-3p-q=29-6\"$
\n" ); document.write( " $\"-5p=23\"$
\n" ); document.write( " $\"p=-23%2F5\"$
\n" ); document.write( "Then use either equation to solve for $\"q\"$
\n" ); document.write( " $\"3%28-23%2F5%29%2Bq=6\"$
\n" ); document.write( " $\"-69%2F5%2Bq=30%2F5\"$
\n" ); document.write( " $\"q=30%2F5%2B69%2F5\"$
\n" ); document.write( " $\"q=99%2F5\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"f%28x%29=%28-23%2F5%29x%2B99%2F5\"$
\n" ); document.write( " $\"-%2823%2F5%29x%2B99%2F5=27\"$
\n" ); document.write( " $\"-%2823%2F5%29x=135%2F5-99%2F5\"$
\n" ); document.write( " $\"-%2823%2F5%29x=36%2F5\"$
\n" ); document.write( " $\"x=-36%2F23\"$
\n" ); document.write( ".
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\n" ); document.write( "The answer of $\"6\"$ doesn't make sense.
\n" ); document.write( "Since the solution is linear and $\"27\"$ is between $\"6\"$ and $\"29\"$ , the solution needs to be between $\"3\"$ and $\"-2\"$ , closer to $\"-2\"$ since $\"27\"$ is closer to $\"29\"$ . My solution is about $\"-1.5\"$ , close compared to $\"-2\"$ . $\"6\"$ is not even in the possible range of solutions.\r
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