The question requires me to check whether the following formulae satisfy the properties of an inner product given the linear space of all real polynomials.

[tex]

f(1)g(1)[/tex]

[tex]\left(\int_{0}^{1}f(t)dt\right)\left(\int_{0}^{1}g(t)dt\right)[/tex]

The properties are satisfied in both cases (at least, that's my answer), but the book says 'No'. How could this be?

[tex]

f(1)g(1)[/tex]

[tex]\left(\int_{0}^{1}f(t)dt\right)\left(\int_{0}^{1}g(t)dt\right)[/tex]

The properties are satisfied in both cases (at least, that's my answer), but the book says 'No'. How could this be?

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