The range of f is derived from the range of f.

2. Matching method: the basic method to find the range of "quadratic function class" by formula method.

3. Inverse function method: using the reciprocal relationship between the definition domain and the value domain of the function and its inverse function, the value domain of the original function is obtained by finding the definition domain of the inverse function.

4. Separation constant method: Both numerator and denominator are rational functions of linear functions of one variable, so separation constant method and inverse function method can be used for this kind of problems.

5. Substitution method: Using algebraic substitution, the awarded function is transformed into another function whose range is easy to determine, thus obtaining the range of the original function.

6. Discriminant method: transform the function into a quadratic equation.

; The equation has real roots, and the discriminant is greater than or equal to 0.

To find the range of the original function,

7. Monotonicity method of function: determine the monotonicity of the function on the definition domain (or a subset of the definition domain) and find the range of the function.

8. Use boundedness: Use the boundedness of some functions to find the range of the original function.

9. Image method (number-type combination method): Function image is an important means to master functions. It is an important method to calculate the function value domain according to the function image by using the combination of numbers. etc