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For f(g(x)) you'll get 3ax+3b+2 and for g(f(x)) you'll get 3ax+2a+b. The equation 3ax+3b+2=3ax+2a+b can be simplified to b+1=a. We also know that ab=20 so the only value where ab=20 and b+1=a is where b=4 and a=5. So your answer is 5.

I am sorry, but that is the wrong answer

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 $a$.

See here: https://web2.0calc.com/questions/help_37093#r2