+0  
 
+1
63
3
avatar+337 

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 \(a\).

 Apr 6, 2020
 #1
avatar+930 
+1

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.

 Apr 6, 2020
 #2
avatar+337 
+1

I am sorry, but that is the wrong answer

 Apr 7, 2020
 #3
avatar+24972 
+1

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

 

laugh

 Apr 8, 2020

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