Question

Let f and g be differentiable functions such that f(x)g(x) = x. Show that f(0) != 0
or g(0) != 0.

Answer 1

okay

Answer 2

f'(x)*g(x)+g'(x)*f(X)=1
if x =0
f'(x)*0+g'(x)*0=1
how is this possible?

Answer 3

unless there is some division by zeros and infinity stuff going on

Answer 4

in which case we cannot say the lim as u approach that point exists so the derivative is not defined

Answer 5

pretty cool

Answer 6

what about he produc t of 3 functions and n fuctions will they also be undefined if they all had evaluated to 0 at x=0

Answer 7

think about that it has the same idea