Projection of a function on another

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I was going through a question paper of an exam and this particular problem caught my eyes. The inner product formula given there is confusing me. I am not getting why there is a additional function multiplied there and what will be a projection of a function on another. I tried to integrate putting $f(x)$ as $1$ and $g(x)$ as $x^2$ and got the inner product but don't know how to proceed from here to get the projection. Click here to see the problem.