f(x)＝e的x^2,f[g(x)]=1-x,且g(x)>=0,求g(x)及其定义域

Question

f(x)＝e的x^2,f[g(x)]=1-x,且g(x)>=0,求g(x)及其定义域

Answer 1

f(x)＝e^(x^2),
则f[g(x)]=e^[g²(x)]=1-x
两边取以e为底的对数得：
g²(x)=ln(1-x)
因为g(x)≧0
所以：g(x)=√ln(1-x),
则ln(1-x)≧0
ln(1-x)≧ln1
1-x≧1
x≦0
所以,定义域为(-∞,0]