and
are real-valued functions defined on the real line. For all
and
.
is not identically zero and
for all
. Prove that
for all
.
%V0
$f$ and $g$ are real-valued functions defined on the real line. For all $x$ and $y, f(x+y)+f(x-y)=2f(x)g(y)$. $f$ is not identically zero and $|f(x)|\le1$ for all $x$. Prove that $|g(x)|\le1$ for all $x$.
Školjka