Let g(x) be the inverse of the function f(x)=ln(e2x +l). Find g(x)and its domain?
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if you apply a function to a number, you get some new number. if you apply the inverse function to that new number, you should get back the original number. in other words, the inverse function undoes the first function.
so if you take x, multiply it by 2, raise that product to e, add l, then take the natural log, you've performed the function f on x. now go backwards in that sentence and perform the opposite functions.
undoing the natural log requires raising e to the power of the number, next subtract l, take the natural log, and finally divide by 2.
hence g(x) = [ln(e^x -l)]/2
as for domain, you know the argument of ln function must be greater than zero, therefore
e^x -l > 0
e^x > l
x > ln(l), where it is assumed whatever the value of l is, it too is greater than 0
so if you take x, multiply it by 2, raise that product to e, add l, then take the natural log, you've performed the function f on x. now go backwards in that sentence and perform the opposite functions.
undoing the natural log requires raising e to the power of the number, next subtract l, take the natural log, and finally divide by 2.
hence g(x) = [ln(e^x -l)]/2
as for domain, you know the argument of ln function must be greater than zero, therefore
e^x -l > 0
e^x > l
x > ln(l), where it is assumed whatever the value of l is, it too is greater than 0
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I don't know what l (the letter L) is. all I can say is that the domain is x > ln(l)
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