Math Gold Medalist

Lor

2023 AMC 12B 

Problem 22

A real-valued function $f$ has the property that for all real numbers $a$ and $b,$\[f(a + b)  + f(a - b) = 2f(a) f(b).\]Which one of the following cannot be the value of $f(1)?$

$\textbf{(A) } 0 \qquad \textbf{(B) } 1 \qquad \textbf{(C) } -1 \qquad \textbf{(D) } 2 \qquad \textbf{(E) } -2$

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   Solution