Question

HELP! True? If as x approaches x0 of lim(f g)(x)=0 then f(x)=0 if approaches x-->x0 or g(x)=o as it approaches x---> x0?

Answer 1

is your question something like this:
if
\[ \large \lim_{x\to x_0}(f\circ g)(x)=0 \]
then
\[ \large \lim_{x\to x_0}f(x)=0\quad\text{or}\quad\lim_{x\to x_0}g(x)=0 \]

Answer 2

yes exactly!

Answer 3

is this true?

Answer 4

give me a second

Answer 5

it is false

Answer 6

here it is the complete justification:
let \(f(x)=x^2-2\) and \(g(x)=x+1\) then
\[ \large (f\circ g)(x)=f(g(x))=f(x+1)=(x+1)^2-2 \]
then
\[ \large (f\circ g)(x)=x^2+2x-1 \]

Answer 7

ok so far?

Answer 8

r u there @Compgroupmail ?

Answer 9

I am here. I'm back now.

Answer 10

can u tell why the proposition if false from what i already did?

Answer 11

yes, I understand now. THanks :) !!

Answer 12

I'll add you as a fan/

Answer 13

well anyway. if u solve \((f\circ g)(x)=0\) u get
\[ \large x=-1\pm\sqrt{2} \]
then
\[ \large \lim_{x\to-1+\sqrt{2}}(f\circ g)(x)=0 \]
but
\[ \large \lim_{x\to-1+\sqrt{2}}f(x)\neq0\quad\text{and}
\lim_{x\to-1+\sqrt{2}}g(x)\neq0 \]