document.write( "Question 1118646: Find f(7)+f^-1(7) if f(3x-2)=x+5 \n" ); document.write( "

Algebra.Com's Answer #734025 by ikleyn(52781) $\"\"$ $\"About$

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document.write( "(1)  To calculate f(7), you need to find a value of x such that 3x-2 = 7.\r\n" );
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document.write( "     You can do it in one line:  3x-2 = 7  ====>  3x = 7+2 = 9  ====>  x = 9/3 = 3.\r\n" );
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document.write( "     Then f(7) = f(3*3-2) = 3 + 5 = 8,  according the given definition of the function f.\r\n" );
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document.write( "(2)  To find  ,  you first find \"x\" from equation x+5 = 7  (left side of the definition of the function f).\r\n" );
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document.write( "     You do it in one line:  x = 7-5 = 2.\r\n" );
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document.write( "     Then you calculate  3x-2  at  x= 2,  and you get  the value  3*2-2 = 6-2 = 4.\r\n" );
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document.write( "     So, f(4) = 7,  which implies    = 4.\r\n" );
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document.write( "(3)  Finally,   +  = 8 + 4 = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Other possible solution\r
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document.write( "(1)  You are given  f(3x-2) = x + 5.\r\n" );
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document.write( "    Introduce new variable  t = 3x-2   and  express  x  via t.\r\n" );
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document.write( "    You will get  x = .\r\n" );
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document.write( "    Thus  f(t) = x + 5 =      (*)\r\n" );
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document.write( "        is the expression (definition) of the given function as the function of \"t\".\r\n" );
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document.write( "     Now  f(7) =  =  = 3 + 5 = 8.\r\n" );
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document.write( "(2)  To find  ,  you need to find which number \"t\" gives the value of 7 to the expression  , which is left side of (*).\r\n" );
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document.write( "     So, you solve the equation   = 7,\r\n" );
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document.write( "     and you do it in one line   = 7 - 5 = 2  ====>  t+2 = 3*2  ====>  t = 3*2 -2 = 4.\r\n" );
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document.write( "     Thus,   = 4,  and you get the same answer as in the first solution above:\r\n" );
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document.write( "      +  = 8 + 4 = 12.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved completely in two ways.\r
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