Inverse hyperbolic sin derivation

[miglo]

Homework Statement

derive the formula inverse sinhx = ln(x+sqrt(x^2+1)) for all real x

Homework Equations

sinhx=(e^x-e^-x)/2 ?

The Attempt at a Solution

i have been staring at this for awhile and i don't know how to start
what should be the first step towards deriving that formula? i just want a hint to get started

 

[Harrisonized]

Let f(x)=(e^x-e^-x)/2

(A function is a map from x→f(x). The inverse is therefore a map from f(x)→x. Therefore, our goal is to isolate x from the above equation.)

f(x)=(e^x-e^-x)/2

2f(x)=e^x-e^-x

2f(x)e^x=(e^x-e^-x)e^x

2f(x)e^x=e^2x-1

0 = e^2x-2f(x)e^x-1

Use the quadratic formula to find e^x.