My question is:(adsbygoogle = window.adsbygoogle || []).push({});

Let [itex]V = \mathbb{R}_1 [x][/itex] be the vector space of polynomials in x of degree at most 1. For [itex]f(x) \, , \, g(x) \in \mathbb{R}_1 [x][/itex], define:

[tex]<f(x) \, , \, g(x)> \, = \int_0^1 x^2 f(x) g(x) dx[/tex]

Show that this defines an inner product on [itex]\mathbb{R}_1[x][/itex]. (You may assume the result which says that for function [itex]h(x) \, , \text{if} \, h(x) \geq 0 \, \, \forall x[/itex], then [itex]\int_0^1 h(x) dx \geq 0[/itex] with equality iff [itex]h \equiv 0[/itex])

I have no idea how to even approach this, can someone point me in the right direction please.

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# Really Stuck! (Inner Product)

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