Solve Linear Equation f(x+a)=f(x^2+a) - Help Needed

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To solve the equation f(x+a) = f(x^2+a), the key is to recognize that both sides must yield the same output for the same input. This leads to the equation x = x^2, which simplifies to x(x-1) = 0, giving solutions x = 0 or x = 1. The discussion also touches on whether linear functions are invertible, suggesting that understanding the properties of linear functions is crucial for solving this type of equation. Clarification on the nature of f(x) could further aid in finding the correct approach. Ultimately, the problem requires identifying values of x that satisfy the equality under the assumption of a linear function.
CBrent
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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?
 
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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
 
CBREnt:
Did your professor say that linear function are..invertible?
 

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