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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.

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.

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