知g(x)=1-2x,f[g(x)]=1-x^2/x^2(x≠0),那么f(1/2)多少

Question

知g(x)=1-2x,f[g(x)]=1-x^2/x^2(x≠0),那么f(1/2)多少

Answer 1

f(1/2)=15
解
f[g(x)]=(1-x^2)/x^2
f(1-2x)=(1-x^2)/x^2
换元法
设1-2x=t
x=(1-t)/2
f(t)=[(1-(1-t)^2/4]/[(1-t)^2/4]
=(3-t)(1+t)/(1-t)^2
∴f(x)=(3-x)(1+x)/(1-x)^2
f(1/2)=(5/2)*(3/2)/(1/4)=15
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