1. ## Subgroup

Hi,

F is the group of numerical functions.
$\displaystyle E={ f_{(a;b)}\in F \ \ /\forall x \in \mathbb{R}/ \ \ f_{(a;b)}(x)=(ax+b)e^{2x} }$
I must show that (H,+) is a subgroup, how to do it please??

2. Originally Posted by lehder
Hi,

F is the group of numerical functions.
$\displaystyle E={ f_{(a;b)}\in F \ \ /\forall x \in \mathbb{R}/ \ \ f_{(a;b)}(x)=(ax+b)e^{2x} }$
I must show that (H,+) is a subgroup, how to do it please??
I don't understand the question.

3. Originally Posted by lehder
Hi,

F is the group of numerical functions.

First "F" you write . Apparently you mean the group of all real functions.

$\displaystyle E={ f_{(a;b)}\in F \ \ /\forall x \in \mathbb{R}/ \ \ f_{(a;b)}(x)=(ax+b)e^{2x} }$

Now you write "E" without curly parentheses $\displaystyle \{,\}$, but you apparently meant $\displaystyle E:=\{f_{(a,b)}\in F\;;\;\forall\,x\in\mathbb{R}\,,\,\,f_{(a,b)}(x):= (ax+b)e^{2x}\}$

I must show that (H,+) is a subgroup, how to do it please??
Now you talk about some "H" (?), which I suppose should be "E", but you don't tell us how the sum "+" is defined there...

Please do check the way you wrote the question and be clearer.

Tonio