A problem from IIT 1981
Let $f(x)$ be a function defined for all x∈R such that $f(x+y)=f(x)⋅f(y)$ for all x,y∈R. Let $f′(0)=3$ and $f(5)=2$. Find the value of $f′(5)$.
The author of http://paramanands.blogspot.in/2010/08/two-problems-from-iit-jee.html#.ViuP3X4rLIU has pointed out that in no way f(x) can be an exponential function.But my question is any such function possible which satisfies the above conditions?Or is the question truly wrong?