Single correct option
A function f(x) = ax + b, with a > 0, satisfies f(f(x)) = 9x + 8 for all real x. What is f(3)?
- A. 9
- B. 13
- C. 11
- D. 17
Show answer and solution
Answer: (C) 11
f(f(x)) = a(ax + b) + b = a²x + ab + b.
Compare with 9x + 8: a² = 9 → a = 3 (since a > 0); ab + b = 4b = 8 → b = 2.
f(x) = 3x + 2, so f(3) = 11.
(With a = −3 we would get −2b = 8, b = −4, but a > 0 rules this out.)
Compare with 9x + 8: a² = 9 → a = 3 (since a > 0); ab + b = 4b = 8 → b = 2.
f(x) = 3x + 2, so f(3) = 11.
(With a = −3 we would get −2b = 8, b = −4, but a > 0 rules this out.)
Saved on this device. Sign in or create a free account to keep it on every device.