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…9, find the sum of all possible values of a.
Post answer w/ explanation please.
Thank you
a(3x+2)+b=3(ax+b)+23ax+2a+b=3ax+3b+22a+b=3b+22a−2b=2a−b=1a−1=b
So as long as a−1=b, f(g(x))=g(f(x)). The only other condition we need to satisfy is ab=20, so:
a(a−1)=20a2−a−20=0(a−5)(a+4)=0a=5,a=−4
Sum them up and you'll get the answer
+140 
