What is the Inverse of the Function f(x) = e^x + e^(-x) + 1?

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SUMMARY

The inverse of the function f(x) = e^x + e^(-x) + 1 can be determined by first setting the equation e^x + e^(-x) + 1 = y. By substituting u = e^x, the problem transforms into a quadratic equation: u^2 + 1 + u(1 - y) = 0. Solving this quadratic for u provides a function of y, from which x can be derived using the natural logarithm: x = ln(u).

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Eishan M
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Hi,
What is the inverse of f(x)= e^x + e^-x +1?
 
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This question has been intimidating me for quite a while. I'm unable to reach a definite conclusion to this. Please help
 
Try solving $$e^x+e^{-x}+1=y.$$
 
Convert problem into a quadratic equation by u=e^x,\ u^2+1+u(1-y)=0. Get u as a function of y, then x=ln(u).
 

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