已知f〔g(x)〕=1+cosx,g(x)=sin(x/2),求f(x)大家教教我_数学解答

已知f〔g(x)〕=1+cosx,g(x)=sin(x/2),求f(x)大家教教我

人气：270 ℃　时间：2020-07-11 07:15:18

解答

f(sin(x/2)) = 1+cosx = 1+（1-2sin(x/2)^2）= 2-2sin(x/2)^2
令sin(x/2)=t,（-1<= t <=1）则f(t)= 2-2*t^2
即f(x) = 2- 2*x^2,(-1<= x <= 1)