Open Question: Is there a difference between saying f(a) is algebraic over F and saying a is algebraic over F?

Open Question: Is there a difference between saying f(a) is algebraic over F and saying a is algebraic over F?

Here is some more information if it helps to undertstand the circumstance.
let f(x) be a nonconstant element of F[x]
a belongs to some extension of F

If they are different can someone please explain to me how becasue they seem like the absolute same to me...

Thank you!


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