If f(x+y) = f(x)*f(y) for all real x,y, then f is exponential. Proof sketch: f(0) = 1 (from setting x=y=0), f(n) = f(1)^n for positive integers (by repeated application), f(rational) extends similarly, and continuity gives f(x) = $a^x$ where a = f(1). JEE problems give f at one point: "if f(3) = 27, find f(5)." Since $a^3$ = 27, a = 3, so f(5) = 3^5 = 243. Variant: f(x+y) = f(x)*f(y) and f'(0) = k gives f(x) = e^(kx). Also note: f(x) > 0 for all x (since f(x) = f$\frac{x}{2}$^2).