A familiar functional equation f(ax+b)=cf(x) will be solved in
the class of functions f:ℝ→ℝ. Applying this result
we will investigate the Hyers-Ulam-Rassias stability problem of the
generalized additive Cauchy equation
f(a1x1+⋯+amxm+x0)=∑i=1mbif(ai1x1+⋯+aimxm) in connection with the question of Rassias and Tabor.