Do not waste your time in derivation every time and use these ones for making problems faster. Learn them.I hope they will be useful. If you like these and want more from me do rate me plz If f(x+y) = f(x).f(y) then f(x)=ax
If f(x+y) = f(x)+f(y) then f(x)=kx
If f(xy) = f(x)+f(y) then f(x)=log x
If f(xy) = f(x).f(y) then f(x)=xn
If f(x+y) = f(x)=f(y), then f(x)=k
If f(x).f(1/x)=f(x)+f(1/x), then f(x)=xn+1
If f(x+y) + f(x-y) = 2f(x)f(y) then f(x)=(ax + a-x)/2 If f(x) is a function such that f(x)f(y)-(f(xy)+f(1/y))/2 = 0 then f(x) = cos(log x) If f(x+y) = f(x)+f(y) then f(n)=n.f(1)