# SOLUTION: Let f(x)= ax+b, where a and b are positive numbers, and assume that the following equation holds for all values of x: f(f(x))= bx+a. Find a+b.

Algebra ->  Algebra  -> Functions -> SOLUTION: Let f(x)= ax+b, where a and b are positive numbers, and assume that the following equation holds for all values of x: f(f(x))= bx+a. Find a+b.      Log On

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 Algebra: Functions, Domain, NOT graphing Solvers Lessons Answers archive Quiz In Depth

 Question 627113: Let f(x)= ax+b, where a and b are positive numbers, and assume that the following equation holds for all values of x: f(f(x))= bx+a. Find a+b.Answer by richard1234(5390)   (Show Source): You can put this solution on YOUR website! . Equate terms with "x" in it, as well as constants: and Substitute b with a^2 in the second equation: . Solving for a, (here, denotes the golden ratio) Since b = a^2, Therefore,