document.write( "Question 1182908: Given that f : x maps to ax + b and f^3 : x maps to 27x + 26, Find the value of a and of b, Find an expression for f^4 \n" ); document.write( "

Algebra.Com's Answer #813015 by ikleyn(52781) $\"\"$ $\"About$

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\n" ); document.write( "Given that f : x maps to ax + b and f^3 : x maps to 27x + 26,
\n" ); document.write( "Find the value of a and of b, Find an expression for f^4
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document.write( "f^2(x) = a*(ax+b) + b = (a^2)x + ab + b.\r\n" );
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document.write( "f^3(x) = (a^2)*(ax+b) + ab + b = (a^3)x + (a^2)*b + ab + b = 27x + 26.\r\n" );
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document.write( "From the last equation,  a^3 = 27;  hence,  a =  = 3.\r\n" );
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document.write( "Then we have\r\n" );
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document.write( "    3^2*b + 3b + b = 26,   or   9b + 3b + b = 26,   13b = 26,  b = 26/13 = 2.\r\n" );
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document.write( "So,  f(x) = 3x + 2.\r\n" );
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document.write( "Finally,  f^4(x) = 27(3x+2) + 26 = 81x + 54 + 26 = 81x + 80.    <<<---===  I just edited this line after the notice by @robertb.   Thanks (!)\r\n" );
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document.write( "ANSWER.  a= 3;  b= 2;   f^4(x) = 81x + 80.\r\n" );
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