document.write( "Question 1190029: Assume f is a one-to-one function. If f(x)=3-6xf , find f^-1(33)
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Algebra.Com's Answer #821555 by ikleyn(52781)\"\" \"About 
You can put this solution on YOUR website!
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\n" ); document.write( "Assume f is a one-to-one function. If f(x)=3-6xf , find f^-1(33)
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\n" ); document.write( "\n" ); document.write( "The problem is presented very unprofessionally in this post.\r
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\n" ); document.write( "\n" ); document.write( "If f(x) = 3 - 6x, then f(x) is a linear function of x. Since a coefficient at x is not equal to zero, \r
\n" ); document.write( "\n" ); document.write( "this function is one-to-one without any assumption: you don't need make this assumption - it is TRUE without any assumption.\r
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\n" ); document.write( "\n" ); document.write( "So, the correct formulation should be in this form:\r
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document.write( "        If f(x)=3-6x, find f^-1(33).\r\n" );
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\n" ); document.write( "\n" ); document.write( "In Math, when you formulate a problem, all the words / (the terms) should be used correctly and must be placed in a right order.\r
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\n" ); document.write( "\n" ); document.write( "It is the same as in music (classic music, I mean . . . )\r
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\n" ); document.write( "\n" ); document.write( "OK, now I will solve the problem. So, the question is\r
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document.write( "    |    If f(x)=3-6x, find f^-1(33).  |\r\n" );
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document.write( "To get the answer, you do not need express f^(-1) (x) explicitly as a function of x.\r\n" );
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document.write( "In this problem, the KEY POINT is to understand that the question is equivalent to finding x from equation\r\n" );
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document.write( "    f(x) = 33,  which is  3 - 6x = 33.\r\n" );
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document.write( "From this equation, you have\r\n" );
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document.write( "    3 - 33 = 6x\r\n" );
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document.write( "      -30  = 6x\r\n" );
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document.write( "       x   = (-30)/6 = -5.\r\n" );
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document.write( "ANSWER.  f^(-1)(33) = -5.\r\n" );
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document.write( "CHECK.   f(-5) = 3 - 6(-5) = 3 + 30 = 33.   ! Precisely correct !\r\n" );
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The lesson to learn from my post

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\n" ); document.write( "\n" ); document.write( "        (1)   To get the answer,  you do not need express  f^(-1) (x)  explicitly as a function of  x.\r
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\n" ); document.write( "\n" ); document.write( "        (2)   In this problem, the question is equivalent to finding x from equation for a base function.\r
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