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if f(x) = ax+b where a and b are real numbers and if f(f(x)) = 9x + 8

then find a+b .

Darkside  Aug 9, 2018
 #1
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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

.

Alan  Aug 9, 2018

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