Grade 12Differential Calculus
Find the inverse of the function f(x)= ln(x+(x^2+1)^1/2).
1 Answer
Arun
Approved Tutor Answer8 Years agoDear 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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