This one has been bothering me for days now. Can anyone help?? Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x.
Follow Math Help Forum on Facebook and Google+
Originally Posted by mathprincess24 This one has been bothering me for days now. Can anyone help?? Show that if f is continuous and f(0) = 1, f(1) = e, and f(x + y) = f(x)f(y) then f(x) = e^x. See this.
how do i know that f(x) = e^x?
Originally Posted by mathprincess24 how do i know that f(x) = e^x? From the "initial conditions" i.e. f(0)=1 and f(1)=e. Do you see how?
yes i understand that when you plug in e^x as the function that all the conditions are met, but how do i prove that its the only one that works. I'm not sure i understand the proof on the bottom half of the link you responded with.
View Tag Cloud