document.write( "Question 828946: Find a linear function f(x) = mx + b such that m is positive and (f(f(x))= 9x + 4.\r
\n" ); document.write( "\n" ); document.write( "The answer is 3x + 1 and I can find this by trial and error. What I want to know is how to reach this answer mathematically.\r
\n" ); document.write( "\n" ); document.write( "I've tried to do it this way: 9x + 4 = m(mx + b) + b = m^2(x) + bm + b but then I got stuck because I have too many unknowns to solve by the quadratic equation.\r
\n" ); document.write( "\n" ); document.write( "Could you please explain this to me?\r
\n" ); document.write( "\n" ); document.write( "Thanks in advance \n" ); document.write( "
Algebra.Com's Answer #499581 by nerdybill(7384)\"\" \"About 
You can put this solution on YOUR website!
f(f(x) = m(mx + b) + b = m^2(x) + bm + b
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\n" ); document.write( "And, they give you:
\n" ); document.write( "f(f(x)= 9x + 4
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\n" ); document.write( "Your two equations are:
\n" ); document.write( "m^2 = 9 (equation 1)
\n" ); document.write( "and
\n" ); document.write( "bm+b = 4 (equation 2)
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\n" ); document.write( "Solving equation 1:
\n" ); document.write( "m^2 = 9
\n" ); document.write( "m = 3
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\n" ); document.write( "Substitute above into equation 2:
\n" ); document.write( "bm+b = 4
\n" ); document.write( "b(3)+b = 4
\n" ); document.write( "4b = 4
\n" ); document.write( "b = 1
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\n" ); document.write( "solution then:
\n" ); document.write( "m = 3 and b = 1
\n" ); document.write( "so
\n" ); document.write( "f(x) = 3x+1\r
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