Problem:
If f(x)=ax+b and f−1(x)=bx+a with a and b real, what is the value of a+b?
Answer Choices:
A. −2
B. −1
C. 0
D. 1
E. 2
Solution:
Since f(f−1(x))=x, it follows that a(bx+a)+b=x, so ab=1 and a2+b=0. Hence a=b=−1, so a+b=−2.
The problems on this page are the property of the MAA's American Mathematics Competitions