Show that

6.C] Show that f(x) = 3x - 2 and g(x) = x are orthogonal in P_n with
\langle f, g \rangle = \int_0^1 f(x)g(x),dx .

Answer:

Show that <span class="wp-katex-eq" data-display="false"> f(x) = 3x - 2 </span> and <span class="wp-katex-eq" data-display="false"> g(x) = x </span> are orthogonal in <span class="wp-katex-eq" data-display="false"> P_n </span> with <span class="wp-katex-eq" data-display="false"> \langle f, g \rangle = \int_0^1 f(x)g(x),dx </span>.

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