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Find the inverse of the function f(x)= ln(x+(x^2+1)^1/2).

Find the inverse of the function f(x)= ln(x+(x^2+1)^1/2).

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Bhavesh
 
The get the inverse, exchange x and y and try to express y in terms of x.
 
x = ln[y + √(y2 + 1)]
 
ex = y + √(y2 + 1)
 
ex - y = √(y2 + 1)
 
Square both sides.
 
e2x - 2exy + y2 = y2 + 1
 
e2x - 2exy = 1
 
y = (1 - e2x) / (-2ex)
 
f-1(x) = (e2x - 1) / (2ex)

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