2018˸߿½ѵ5

ѵ5 ⺯ʽ

⺯ʽǸ߿ص㿼֮һ.Ҫ⺯ĻϣʽļַγĴͽʵ.

ѵų

()֪f(2-cosx)=cos2x+cosx,f(x-1).

̽

[1](1)֪f(x)f(logax)= (a>0,a1,x>0),f(x)ıʽ.

(2)֪κf(x)=ax2+bx+c|f(1)|=|f(-1)|=|f(0)|=1,f(x)ıʽ.

ͼҪ麯еҪأֵͶӦԼۺ֪ʶ.Ŀ.

֪ʶУú֪ʶرǶԡf⣬úõȼתעⶨ.

˼άҪϸߣԶĿ顢ȼת׳.

뷽(1)ûԪ;(2)ôϵ.

⣺(1)t=logax(a>1,t>0;0

f(t)= (at-a-t)

f(x)= (ax-a-x)(a>1,x>0;0

(2)f(1)=a+b+c,f(-1)=a-b+c,f(0)=c

f(1)f(-1)f(0)ͬʱ1-1Ϊf(x)=2x2-1f(x)=-2x2+1f(x)=-x2-x+1f(x)=x2-x-1f(x)=-x2+x+1f(x)=x2+x-1.

[2]f(x)ΪRϵżx-1ʱy=f(x)ͼǾ(-20)бΪ1ߣy=f(x)ͼһǶ(02)ҹ(-11)һߣдf(x)ıʽͼͼ.

ͼҪ麯֪ʶߡߵĻͼԷֶκķҪǿ˼ά.ˣֶκǽ߿ȵ.Ŀ. ֪ʶУżǹؼϵ߷.

˼άҪܸߣۡۺ֪ʶ׷.

뷽з࣬ôϵʽ.

⣺(1)x-1ʱf(x)=x+b

߹(-20).0=-2+bb=2f(x)=x+2.

(2)-1

߹(-11)1=a·(-1)2+2,a=-1

f(x)=-x2+2.

(3)x1ʱf(x)=-x+2

Ͽ֪f(x)= ͼɶ.

ѵ漰⼰ҪУ

1.ϵ֪ʽĹʱôϵ;

2.Ԫշ֪Ϻf[g(x)]ıʽûԪʽϼʱҲշ;

3.η֪ĺʽýⷽεķf(x);

⣬ڽоõۡȼתѧ˼뷽.

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