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已知指数函数y=g（x）满足：g（2）=4，定义域为R的函数f（x）= -g(x)+n 2g(x)+m 是奇函数． （1）确定y=g（x）的解析式； （2）求m，n的值； （3）若对任意的t∈R，不等式f（t 2 -2t）+f（2t 2 -k）＜0恒成立，求实数k的取值范围．
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