document.write( "Question 202896: If (x)=8-3x, then find f^-1 (14). Is it -34, -2, 2, -1/34? please help. thank-you. \n" ); document.write( "
Algebra.Com's Answer #153068 by jsmallt9(3758)\"\" \"About 
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The notation \"f%5E%28-1%29%28x%29\" stands for \"the inverse of f(x)\". The inverse of f(x) is the relation you get when you swap the x and y in the equation for f(x). (Note: The Algebra.com's software incorrectly puts a multiplication symbol in the middle of \"f%5E%28-1%29%28x%29\". Please ignore it.)

\n" ); document.write( "We'll start by figuring out \"f%5E%28-1%29%28x%29\" and then use it to find \"f%5E%28-1%29%2814%29\".

\n" ); document.write( "To find the inverse of f(x):
  1. Rewrite it with a \"y\" in the place of f(x):
    \n" ); document.write( "\"y+=+8+-+3x\"
  2. Rewrite the equation with x's where the y's are and y's are the x's are:
    \n" ); document.write( "\"x+=+8+-3y\"
    \n" ); document.write( "This is the inverse equation.
  3. Solve the inverse equation for y:
    \n" ); document.write( "Subtract 8 from both sides:
    \n" ); document.write( "\"x+-+8+=+-3y\"
    \n" ); document.write( "Divide both sides by -3:
    \n" ); document.write( "\"%28x+-+8%29%2F%28-3%29+=+y\"
  4. Replace the \"y\" with \"f%5E%28-1%29%28x%29\":
    \n" ); document.write( "\"%28x+-+8%29%2F%28-3%29+=+f%5E%28-1%29%28x%29\"

\n" ); document.write( "Now we will find \"f%5E%28-1%29%2814%29\":
\n" ); document.write( "\"f%5E%28-1%29%2814%29+=+%28%2814%29+-+8%29%2F%28-3%29\"
\n" ); document.write( "Simplifying we get
\n" ); document.write( "\"f%5E%28-1%29%2814%29+=+6%2F%28-3%29\"
\n" ); document.write( "\"f%5E%28-1%29%2814%29+=+-2\"
\n" ); document.write( " \n" ); document.write( "
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