Solving f(x+a)=f(x^2+a) for x with a linear function

[CBrent]

We are studying linear equations in school and the prof gave us this to solve for extra credit:

f(x+a) = f(x^2+a)
what is x?

I don't know what type of equation that is, so I can't even start a solution. Can anyone help guide me in the right direction?

 

[IBY]

Well, what number do you have to plug into x to get:
$$x=x^2$$?
Because, since both are the same functions, then the numbers being inserted, assuming it is a linear function, must be the same, so:
$$x+a=x^2+a$$

 

[arildno]

CBREnt:
Did your professor say that linear function are..invertible?