# How to show if a function is partial recursive?

I have seen and understood the most definitions but i just could not understand how to show if a function is mu-partial recursive or not. I used search engines, but all I find are just more lectures with definitions...

Lets say I have a function like

f(x) = x^2


or

f(x)=root(x+5) + 5


Can you proof if those functions are mu-partial recursive? Explain why this function is mu-partial recurisve.

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show that x is partial recursive and the product of two partial recursive is partial recursive. Then show the sum of two partial recursive is partial recursive, and show root is partial recursive. – user51427 Dec 9 '12 at 0:33
Thx for comment!! but this is right now to difficult for me. I see all the definitions with variables, but i need one real example with real numbers :/. Something like a cookbook example – Gero Dec 9 '12 at 0:35
Recursive functions are, officially, only defined on natural numbers. You'll have to be more precise about what you mean by a recursive real-valued function. – Zhen Lin Dec 9 '12 at 0:37
hmm ok, can you show if f(x)=root(x+5) + 5 is mu-partial recursive? step by step – Gero Dec 9 '12 at 0:39
Exactly what definition you want to verify? – Berci Dec 9 '12 at 3:02