1、f(x)=4x？ -kx-8 =4(x-k/8)？ -k？ / 16-8

The image is a parabola with an upward opening, and the equation of symmetry axis is x=k/8.

In order to make the function monotonous, the symmetry axis cannot fall within the interval (5, 20).

K/8≤5 or k/8≥20

∴k≤40 or k≥ 160

The range of real number k is (-∞, 40]∩[ 160,+∞);

2.( 1) doesn't even work for the following reasons:

f(x)=x^(-2)= 1/x？

f(-x)= 1/(-x)？ = 1/x？

∴f(-x)=f(x)

So y = x (-2) is an even function,

(2) Regarding the Y-axis symmetry, the reason: f(-x)=f(x),

(3)y=x？ On (0, +∞) is an increasing function,

∴f(x)=x^(-2)= 1/x？ It is a decreasing function on (0, +∞).

(4)y=x？ It is a decreasing function on (-∞, 0),

∴f(x)=x^(-2)= 1/x？ On (-∞, 0) is increasing function;

3. Let point D be DE⊥AB and point E be | DE | = H.

In the circle o, there is: ∠ ADB = 90.

∴BD=√( 16-x？ )

According to the equal area, there are: AB*DE=AD*BD.

∴4*h=x*√( 16-x？ )

h=x*√( 16-x？ )/4

At △ADE, AE? =AD？ De?

∴|AE|=√(x？ -h？ )=x？ /4

|CD|=4-a？ /2

Circumference y=|AB|+|CD|+2|AD|

=4+4-x？ /2+2 times

=-x？ /2+2x+8

|AE|=x？ /4 < 2, that is, X.