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Let f(x) = px+q, where p and q are real numbers. Find p+q if f(f(f(x))) = 8x+21.

 Jun 20, 2019
 #1
avatar+104962 
+1

f(f(x))  =   p (px + q) + q

 

f (f(f(x)))  =  p [ p (px + q) + q ] + q   =

 

p [ p^2x + pq + q ] + q  =

 

p^3x + p^2q + pq + q   = 8x + 21

 

This implies that

 

p^3x  = 8x

 

p^3  =8

 

p = 2

 

And

 

p^2q + pq + q  = 21     ....so....

 

(2)^2q  + 2q + q  = 21

 

4q + 2q + q  =  21

 

7q  =  21

 

q  = 3

 

So

 

p + q  =   2 + 3    =    5

 

 

 

cool cool cool

 Jun 20, 2019
 #2
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+1

Thank you so much!

 Jun 20, 2019

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