(1) It is known that the domain of f(x) is [1, 3]. Find the domain of f (2x- 1).
The definition of f(x) is [1, 3], that is, in f(x), x ∈ [1, 3], then:
F (2x+ 1)，2x+ 1 ∈ [ 1，3]，x ∈ [0， 1]。
Then:
In f (2x+ 1), x ∈ [0, 1] so the domain of f (2x+ 1) is [0, 1].
Note: Function domain: a mathematical term, which is one of the three elements of a function (domain, range and corresponding law) and the object of corresponding law. Refers to the value range of function independent variables, that is, for two non-empty sets D and M with corresponding functions, any number in set D has only one definite number corresponding to it, so set D is called function domain.
A function formed by several basic functions through four operations, whose domain is a common part that makes all parts meaningful.
Definition domain refers to the value range of independent variable X, which is one of the three elements of a function (definition domain, value domain and corresponding rule) and the object of corresponding rule. Finding the domain of function mainly includes three kinds of problems: abstract function, general function and function application.