ѵ7 ż뵥(һ)
ĵԡżǸ߿ص֮һ.ҪżԡԵĶ壬жȷʶżͼ.
ѵų
()a>0,f(x)= Rϵż(1)aֵ;(2)֤ f(x)(0+).
̽
[1]֪f(x)(-11)ж壬f( )=-1,ҽ0
(1)f(x)Ϊ溯;(2)f(x)(-11)ϵݼ.
ͼҪ麯żԡԵжԼ.Ŀ.
֪ʶУżԼԶ弰жֵת˼.
˼άҪϸߣֵȷ㼼ܲأѻ.
뷽(1)f(0)ֵȡx=-yǽؼ;(2)ж ķΧǽ.
֤(1)f(x)+f(y)=f( ),x=y=0,f(0)=0,y=-x,f(x)+f(-x)=f( )=f(0)=0.f(x)=-f(-x).f(x)Ϊ溯.
(2)֤f(x)(01)ϵݼ.
0
00,1-x1x2>0 >0,
(x2-x1)-(1-x2x1)=(x2-1)(x1+1)<0
x2-x1<1-x2x1,
0< <1,֪f( )<0
f(x2)
f(x)(01)Ϊf(x)Ϊ溯f(0)=0.
f(x)(-11)Ϊ.
[2]躯f(x)ǶRϵż(-,0)ڵf(2a2+a+1)
ͼҪ麯żԡԵĻӦԼԸϺԵж.ڡＶĿ.
֪ʶУʶżԡԡָĵԼֵ.
˼ά衢ʶϺж.
뷽֪ʶ࣬ؼڶж˼ʶͨ࣬һ㼼뷽.
⣺0
f(-x2)
f(x2)
f(2a2+a+1)3a2-2a+1.֮0
a2-3a+1=(a- )2- .
ຯy=( ) ĵ[ +]
0
ѵ漰⼰ҪУ
(1)жϺż뵥
Ϊ庯ϸնжϣע任еĵȼ.
ΪжĻϣúøֵע⸳ֵĿѧԡ.
ͬʱעж֤ߵеġųѵᣬúεͳһ.
Ϻżԡ.ĽؼڣȰոϹ̣ջ.
(2)ǿ˼άͳһ.ϽӦĿһǽչоżԡԵӦ.
2017ɿ⣺2017˸߿ʷƾѧģ
2017ɿ2017˸߿ʱ/
