设f(x)=1+lgx,g(x)=x^2,那么使2f【g(x)】=g【f(x)】的x值是
问题描述:
设f(x)=1+lgx,g(x)=x^2,那么使2f【g(x)】=g【f(x)】的x值是
答案是10^(1+根号2)和10^(1-根号2)
答
f(g(x))=1+lgx²=1+2lgx,g(f(x))=(1+lgx)²=(lgx)²+2lgx+1而2f(g(x))=g(f(x)),那么2(1+2lgx)=(lgx)²+2lgx+1化简,得:(lgx)²-2lgx-1=0所以lgx=1+√2,或lgx=1-√2那么x=10^(1+√2),或x=10^(1-...