If \(f(x)\) is a linear polynomial such that
\[
f(ax+by)=af(x)+bf(y)
\]
for all \(x,y\in\mathbb{R}\). If \(f(0)=7\) and \(f'(0)=5\), then
\[
\frac{f(1)+f(-1)}{a+b}=
\]
Show Hint
For a linear polynomial,
\[
f(x)=mx+c,
\]
\[
\boxed{m=f'(x)=f'(0),\qquad c=f(0).}
\]
In functional equations, substitute the polynomial directly and compare coefficients or constant terms to obtain unknown parameters.