Proving that a function f(n) belongs to a Big-Theta(g(n))

Posted by PLS on Stack Overflow See other posts from Stack Overflow or by PLS
Published on 2010-04-27T04:05:49Z Indexed on 2010/04/27 4:13 UTC
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asymptotic-complexity

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big-theta

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inequality

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homework

Its a exercise that ask to indicate the class Big-Theta(g(n)) the functions belongs to and to prove the assertion.

In this case f(n) = (n^2+1)^10

By definition f(n) E Big-Theta(g(n)) <=> c1*g(n) < f(n) < c2*g(n), where c1 and c2 are two constants.

I know that for this specific f(n) the Big-Theta is g(n^20) but I don't know who to prove it properly. I guess I need to manipulate this inequality but I don't know how

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