Special Functions

[mtiller1]

In learning trig functions, we had to be told that 5/3+4 was NOT the same as 5/3 + 5/4 (luckily I knew that much :wink: ); however he said that there is one category of "very special" functions that follow the form:

f(x+y) = f(x) + f(y)

Anyone know?

Thanks,
Angel

 

[Unco]

Let f(x) = x.

So f(y) = y.

And f(x + y) = x + y = f(x) + f(y)

:lol:

 

[soroban]

Hello, Angel!

In learning trig functions, we had to be told that \(\displaystyle \frac{5}{3+4}\) was NOT the same as \(\displaystyle \frac{5}{3}\,+\,\frac{5}{4}\) (luckily I knew that much.)

However, he said that there is one category of "very special" functions that follow the form:

\(\displaystyle f(x\,+\,y)\:=\:f(x)\,+\,f(y)\)

Anyone know?

I can think of one type.

. . For example: .\(\displaystyle f(x)\,=\,3x\)

 

[stapel]

...there is one category of "very special" functions that follow the form "f(x+y) = f(x) + f(y)" Anyone know?

Are you asking for examples of such functions? The name of this sort of function? What is it that you're asking if we know?

Thank you.

Eliz.

 

[mtiller1]

Are you asking for examples of such functions? The name of this sort of function? What is it that you're asking if we know?

I need to understand the concept, so I guess an explanation of an example (was that clear as mud or what?!?).

Thanks for any help!
Angel

 

[stapel]

I need to understand the concept....

Um... "the concept" of what? That a certain thing exists...? This has already been shown (by giving examples).

Please reply with clarification. Thank you.

Eliz.