First, the domain of composite function.

If the definition domain of function y=f(u) is b and that of u = g (x) is a, the definition domain of compound function y=f is D={x|x∈A, and g(x)∈B} comprehensively considers the range of values of each part of x and takes its intersection.

1, the range of r when it is an algebraic expression or an odd root.

2. When it is an even number of roots, the number of roots is not less than 0 (i.e. ≥0).

3. When it is a fraction, the denominator is not 0; When the denominator is an even root, the number of roots is greater than 0.

4. When it is exponential, the base is not 0 for zero exponential power or negative integer exponential power.

5. When some basic functions are composed of four operations, its domain should be a set of independent variable values that make each part meaningful, that is, to find the intersection of the domain sets of each part.

6. The domain of piecewise function is the union of independent variable sets on each segment.

7. For the function established in practical problems, we should not only consider making the analytical expression meaningful, but also consider the requirements of practical significance for the independent variables.

8. For the function with parameter letters, it is generally necessary to classify and discuss the values of letters when finding the domain. Note that the domain of the function is a non-empty set.

9. The truth value of logarithmic function must be greater than zero, and the radix must be greater than zero and not equal to 1.

Second, the common problems of composite function

1, the domain of f(x) is known as a, and the domain of f is found: in essence, the domain of g(x) is known as a, so the domain of x can be found.

2. Given that the domain of F is B, find the domain of f(x): In essence, the domain of X is known as B, so as to find the domain of g(x).

3. Knowing that the domain of F is C, finding the domain of F: In essence, knowing that the domain of X is C, so as to find the domain of g(x) first (that is, the domain of f(x)); Then take it as the range of h(x), and then find the range of x.