1. The absolute value range of the function Y=4-X is (4, negative infinity), that is, y.

2. If the function f(x)=ax? +(a+ 1)x+ 1 is an even function, so use f(-x)=f(x) to solve the problem of a=- 1.

3. The domain of the function f(x)= radical sign (x-2)/(2x+ 1) is x; 7/2

This problem is solved by the fact that the number of quadratic roots is greater than 0 and the denominator is not equal to 0.

4.

(1) function relation y=( 12x-x? )/2

(2)

Solution: The domain of function Y is (0, positive infinity).

Find the derivative of y y'=6-x

Let y'=0 and solve x=6.

List: x (0 0,6) 6 (6, positive infinity)

y' + 0 -

As y increases, the maximum decreases.

Therefore, when the length of the garden is x=6 and the width is 3, the maximum area of the garden is y= 18.