路径一:正确理解函数概念是解决有关函数问题的关键.路径一:正确理解函数概念是解决有关函数问题的关键.例1已知函数f(x)的定义域是[0,1],求f(x2)的定义域。分析:要解决这一问题需明确:(1)定义域是自变量x的取值范围;(2)f(x)制约的是x,而f(x2)制约的是x2.解:由不等式0≤x2≤1得-1≤x≤1,即函数f(x2)的定义域为[-1,1].路径二:函数的性质是由x的变化决定的,如奇偶性、单调性都是针对x而言的,而不是针对x的某个表达式. Path One: Correctly understanding the concept of a function is the key to solving a function problem. Path One: Correct understanding of the concept of a function is the key to solving a function problem. Example 1 The domain of the known function f(x) is [0,1]. The domain of f(x2). Analysis: To solve this problem, it is necessary to clarify: (1) The definition domain is the range of values ​​of the independent variable x; (2) f(x) is the constraint of x, and f(x2) is the constraint of x2. Solution: Inequality 0≤x2≤1 has -1≤x≤1, that is, the domain of the function f(x2) is [-1,1]. Path 2: The nature of the function is determined by the change of x, such as parity, monotonicity. It’s all about x, not an expression for x.