MHB Understanding the Meaning of "D_g" and "D_f" Symbols

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The symbols $$D_g$$ and $$D_f$$ refer to the domains of the functions g and f, respectively. Specifically, $$D_g$$ represents the set of all values of x for which the function g(x) is defined. The discussion confirms that this interpretation is correct, with participants expressing appreciation for the clarification. Understanding these symbols is essential for grasping function definitions in mathematical contexts. The conversation highlights the importance of recognizing function domains in mathematical analysis.
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Hello MHB,
I am reading about a rule which I got no clue what it's name is on english but I think that you Will understand.
2d1vi2t.jpg

My question is what do they mean with that $$D_g$$ and $$D_f$$

Regards,
$$|\pi\rangle$$
 
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Re: Understanding a symbole

Petrus said:
My question is what do they mean with that $$D_g$$ and $$D_f$$

Looks like $D_g$ means the domain of g.
That is the set of all values of x for which g(x) is defined.
 
Re: Understanding a symbole

I like Serena said:
Looks like $D_g$ means the domain of g.
That is the set of all values of x for which g(x) is defined.
Thanks! That Was what I thought aswell! Thanks for taking your time!😊
Regards,
$$|\pi\rangle$$
 

Thread 'Proving that convexity implies second order derivative being positive'

There are probably loads of proofs of this online, but I do not want to cheat. Here is my attempt: Convexity says that $$f(\lambda a + (1-\lambda)b) \leq \lambda f(a) + (1-\lambda) f(b)$$ $$f(b + \lambda(a-b)) \leq f(b) + \lambda (f(a) - f(b))$$ We know from the intermediate value theorem that there exists a ##c \in (b,a)## such that $$\frac{f(a) - f(b)}{a-b} = f'(c).$$ Hence $$f(b + \lambda(a-b)) \leq f(b) + \lambda (a - b) f'(c))$$ $$\frac{f(b + \lambda(a-b)) - f(b)}{\lambda(a-b)}...
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