f(x)=-f(-x)=-(2*-x-(-x)^2)=2x+x^2

f(X)=2x-x？ x≥0

f(x)=2x+x^2 x & lt； 0

2.

Because 0

Its symmetry axis is X= 1.

Classified discussion

One. 0<a & ltB≤ 1, then the function in this interval is increasing.

f(a)= 1/b=2a-a？

f(b)= 1/a=2b-b？

A=b= 1 shed

Two. 0 & lta≤ 1≤b≤2

When x= 1, there is a maximum value of 1.

1/a= 1

a= 1

Then x=b has a minimum value.

f(b)= 1/b=2b-b？

After sorting, (b- 1) (b 2-b- 1) = 0.

The solution is B= 1 shed.

Or B=( 1- radical number 5)/2 shed.

Or B=( 1+ radical number 5)/2.

So a= 1, b=( 1+ root number 5)/2.

Three. 1≤a & lt； B≤2, then the function in this interval is decreasing.

So f(a)= 1/a=2a-a?

f(b)= 1/b=2b-b？

A= 1, b=( 1+ root number 5)/2.

finally

A= 1, b=( 1+ root number 5)/2.