Solve logarithmic equation for x to find the inverse of f(x)= ln(x+sqrt(x^2+1))

Cortez Clarke

Cortez Clarke

Answered question

2022-11-18

Solve logarithmic equation for x to find the inverse of f ( x ) = ln ( x + x 2 + 1 )

Answer & Explanation

Brooklyn Mcintyre

Brooklyn Mcintyre

Beginner2022-11-19Added 18 answers

Let y = ln ( x + x 2 + 1 ), then:
e y = x + x 2 + 1
e y x = x 2 + 1
( e y x ) 2 = ( x 2 + 1 ) 2
e 2 y 2 x e y + x 2 = x 2 + 1
e 2 y 2 x e y = 1
e 2 y 1 = 2 x e y
x = e y e y 2
So f 1 ( y ) = e y e y 2 .

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