SOLUTION: Suppose that f(x) = ax + b, where a and b are real numbers. Given that f(f(f(x))) = 8x + 21, what is the value of a + b?

Algebra ->  Functions -> SOLUTION: Suppose that f(x) = ax + b, where a and b are real numbers. Given that f(f(f(x))) = 8x + 21, what is the value of a + b?      Log On


   

Question 257618: Suppose that f(x) = ax + b, where a and b are real numbers.
Given that f(f(f(x))) = 8x + 21, what is the value of a + b?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Hint: Starting with f%28x%29=ax%2Bb, plug in ax%2Bb for 'x' to get f%28f%28x%29%29=a%28ax%2Bb%29%2Bb. Do so again to get f%28f%28f%28x%29%29%29=a%28a%28ax%2Bb%29%2Bb%29%2Bb. Now simplify to get f%28f%28f%28x%29%29%29=a%5E3x%2Ba%5E2b%2Bab%2Bb. From here, just equate the two expressions and solve for 'a' and 'b'.