AMC 12 2023 B Problem 22

A real-valued function f has the property that for all real numbers a and b,
f(a+b)+f(a-b)=2 f(a) f(b)

Which one of the following cannot be the value of f(1)?

Answer Choices
A. 0
B. 1
C. -1
D. 2
E. -2