Function inner product

  • Thread starter Asuralm
  • Start date
  • #1
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Main Question or Discussion Point

Dear all:
I have a problem about the inner product of a function. Give a function

[tex]
\begin{displaymath}
f(x) = \left\{ \begin{array}{ll}
x & \textrm{if $x \in [0,1]$}\\
-x+2 & \textrm{if $x \in (1, 2]$}
\end{array}
\end{displaymath}
\{[/tex]

What's the value of the inner product of the function itself over [0,2]?
[tex]
\begin{displaymath}
<f(x), f(x)> = \int_{x=0}^{x=2} f(x)f(x) d_x
\end{displaymath}
[/tex]]

If given another function
[tex]

g(x) = \left\{ \begin{array}{ll}
x-1 & \textrm{if $x \in [1,2]$}\\
-x+3 & \textrm{if $x \in (2, 3]$}
\end{array}

\{[/tex]

What's the inner product of f(x) and g(x) please?

Thanks for answering.
 
Last edited:

Answers and Replies

  • #2
90
0
For you first question you have to seperate integral into two
One of them is from 0 to 1, the other is from 1 to 2.

For the second you have to explain on which interval we take the inner product they are from different worlds.
 
  • #3
35
0
I know the principle actually. Could you give me the whole details please? Because I can't get the correct answer.
 
  • #4
90
0
For question1
You have to get from integral(0-1) =1/2 and from integral(1-2) =1/3
If you did not then write what you did .Maybe we can find the mistake
It would be yours or mine
 
Last edited:
  • #5
90
0
for question 2 : I am still waiting an explanation
It can be only defined on [1,2] i think
 
Last edited:
  • #6
263
0
It's possible that the intention is that f and g vanish wherever not explicitly defined. Then you would be right, it would be like on [1,2]...
 

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