Let f(x) = ax + b where a and b are integers. If f(f(x)) = 16x − 15, what is a possible value for a + b? A. 1 B. −7 C. 9 D. Both 1 and 9 Answer: A) 1 Explanation: f(f(x)) = a(ax+b)+b = a²x + ab + b. Equating coefficients: a² = 16 → a = 4 or −4. If a = 4, 4b+b = −15 → 5b = −15 → b = −3. Sum = 1. If a = −4, −4b+b = −15 → −3b = −15 → b = 5. Sum = 1.

imo class 12 relations and functions

Let f(x) = ax + b where a and b are integers. If f(f(x)) = 16x − 15, what is a possible value for a + b?

VAVidaara Admin Asked 6d ago 0 views 0 answers

#IMO #Class 12 #Mathematics #Relations and Functions #achievers

Let f(x) = ax + b where a and b are integers. If f(f(x)) = 16x − 15, what is a possible value for a + b?

A. 1
B. −7
C. 9
D. Both 1 and 9

Answer: A) 1

Explanation: f(f(x)) = a(ax+b)+b = a²x + ab + b. Equating coefficients: a² = 16 → a = 4 or −4. If a = 4, 4b+b = −15 → 5b = −15 → b = −3. Sum = 1. If a = −4, −4b+b = −15 → −3b = −15 → b = 5. Sum = 1.

0 Answers

Discussion (0)

No comments yet — start the discussion.

← Back to all questions