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Let $f(x)=3x+2$ and $g(x)=ax+b$, for some constants $a$ and $b$. If $ab=20$ and $f(g(x))=g(f(x))$ for $x=0,1,2\ldots 9$, find the sum of all possible values of $a$.

 
 Jan 8, 2021
 #1
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Soluiton by computer program:

 

f(x) = 3x + 2

g(x) = ax + b

 

for (1 <= a <= 20)

for (1 <= b <= 20)

  if (a*b == 20)

    if (f(g(x)) = g(f(x)) for 0 <= x <= 9) output(a)

 

output = 2, 3, 4, 5

 

Sum of all possible a = 2 + 3 + 4 + 5 = 14.

 
 Jan 8, 2021
 #2
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sorry, I tried that answer and it is incorrect.

 
Guest Jan 8, 2021

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