Variational methods - conjugate of function

[braindead101]

Let F->R bar be a function and F*->R bar its conjugate. Fix aEH and show that the conjugate of the new function G(u)=F(u-a) is G*(u*)=F*(u*)+<a,u>
Verify the case where F:R^2->R, F(x)=1/2(x)^2 and a = (2,-1)

I don't really know how to show this. please help

 

[HallsofIvy]

First, define your terms. What kind of objects are H and R? Euclidean spaces? General vector spaces? Hilbert spaces? Is "R", at least, the set of real numbers? The fact that you then use R² as a specific case implies that it is. Is <a, u> the inner product in H? Finally, what, precisely, is your definition of "conjugate"?