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Algebra/Algebra Problem with Functions

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Question
I am really stuck on the following problem.  I just don't know how to set up a path for the solution.  Could you please guide me?

Given that f(x^2 + 1) = 2x + f(x) for all real x and f(0) = 7, find the value of f(5).

I looked at: f(x^2 + 1) = 2x + 7. But that leads me nowhere.  So, I solved x^2 +1 = 2x + 2x +1 for x.  I found that x = 0 and x = 4.  This is where I am stuck.

Thanks,
Jimmy

Answer
For  f(x^2 + 1) = 2x + f(x), we shall consider a series of substitutions to help us out.

substituting in x=0, we have
   
    f(1) = 2* 0 +  f(0) = 7

substituting in x=1,

    f(1^2 + 1) = f(2) = 2 * 1 + f(1) = 2 + 7 = 9   ( it is known previously that f(1) = 7 )   

substituting in x=2,

     f(2^2 + 1) = f(5) = 2* 2 + f(2) = 4 + 9         ( it is known previously that f(2) = 9 )   

         = 13 (shown)

Hope this helps. Peace.

Algebra

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