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**transgalactic** $\displaystyle <f,g>=3\int^{0}_{2}f(x)\overline{g(x)}dx +f(1)\overline{g(1)}\\$

$\displaystyle \overline{<f,g>}=\overline{3\int^{0}_{2}f(x)\overl ine{g(x)}dx +f(1)\overline{g(1)}}=3\int^{0}_{2}\overline{f(x)} g(x)dx +\overline{f(1)}g(1)=<g,f>\\$

i proved too that <f,f> =>0

how to prove <f,f>=0 if f=0

??

$\displaystyle <f,f>=3\int^{0}_{2}f(x)\overline{f(x)}dx +f(1)\overline{f(1)}=3\int^{0}_{2}{||f(x)||}^2dx +{||f(1)||}^2\\$

which is bigger that 0

so i disproved it

?