Y=ln(x+根号下x^2+1)的反函数,急救
2016-09-22
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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)
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)
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