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.