Thread: Real Analysis Help!!

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.

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.