April 05.08.2007 12:19 Let $ f$ be a function given by $ f(x) = \lg(x+1)-\frac{1}{2}\cdot\log_{3}x$. a) Solve the equation $ f(x) = 0$. b) Find the number of the subsets of the set \[ \{n | f(n^{2}-214n-1998) \geq 0,\ n \in\mathbb{Z}\}.\]
Rust 05.08.2007 13:35 $ f(x)$ defined for $ x>0$ and $ f(x)>0,x<9,f(x)<0,x>9.$ a) x=9; b) equavalent to (*) $ 0<n^{2}-214n-1998\le 9$. Only $ n=116$ is solution (*)
Benz 06.08.2007 05:03 I think (*) has the following solutions: x=-9, x=-10, x=-11, x=223, thus the answer to (b) is 16 (the empty set is a subset of every set).