Y=ln(x+根号下x^2+1)的反函数,急救

2024-12-03 13:53:12
推荐回答(2个)
回答1:

Y=ln【(x+√(x²+1)】
x+√(x²+1) = e^y
√(x²+1) = e^y - x

x²+1 = (e^y - x)²

x²+1 = e^2y - 2xe^y+x²

1 = e^2y - 2xe^y

2xe^y = e^2y - 1

x = (e^2y-1)/(2e^y) = e^y/2 - 1/{2e^y)

即,反函数:
y = e^x/2 - 1/{2e^x)

回答2:

简单计算一下,答案如图所示