Multiplicative Functional Equation

f(xy) = f(x)f(y)
In this video, I solve the following neat question: Find all continuous functions f such that f(xy) = f(x) f(y). One solution would be f(x) = x^2, but can you think of other ones? I solve this with a clever transformation, by reducing this equation to one that is more familiar. I also discuss the case where x and y are 0 and/or negative, and even mention the non-continuous case. Enjoy!
Other functional equations:
f(x+y) = f(x) + f(y): • fx+y = fx + fy (Cauchy's functional equation)
f(x+y) = f(x)f(y): • f(x+y) = f(x)f(y)
f(f(f(x))) = x: • Press fff to pay respects
f'(x) = f(f(x)): • A new hard differentia...
Subscribe to my channel: / drpeyam
Check out my Teespring merch: teespring.com/...