if f(x) = ax+b where a and b are real numbers and if f(f(x)) = 9x + 8
then find a+b .
f(x) = ax + b means that f(f(x)) = a(ax+b) + b
So f(f(x)) = a2x + ab + b
If this equals 9x + 8 then we must have a2 = 9, so a = 3 (or -3) and ab + b = 8
With a=3: 3b + b = 8, so b = 2
With a=-3: -3b + b = 8, so b = -4
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+295 
