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

Algebra ->  Rational-functions -> SOLUTION: : Let f(x)=px+q, where p and q are real numbers. Find p+q if f(f(f(x)))=8x+21. Thank you. Thank you.       Log On


   

Question 919994: : Let f(x)=px+q, where p and q are real numbers. Find p+q if f(f(f(x)))=8x+21. Thank you. Thank you.
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
f(f(f(x))) = f(f(px+q)) = f(p(px+q) + q) = p(p(px+q) + q) + q = 8x + 21

We see that the x coefficient is p^3 = 8, so p = 2. If we let x = 0, for example, we have

2(2(2*0 + q) + q) + q = 21
2(2(q) + q) + q = 21
7q = 21
q = 3