# SOLUTION: Find the inverse of the following function. Find domain, range, and asymptotes of each function. f(x)=ln(x+1)+1 I tried to solve this but i got mixed up. Here is what I had.

Algebra ->  Algebra  -> Inverses -> SOLUTION: Find the inverse of the following function. Find domain, range, and asymptotes of each function. f(x)=ln(x+1)+1 I tried to solve this but i got mixed up. Here is what I had.       Log On

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 Question 616249: Find the inverse of the following function. Find domain, range, and asymptotes of each function. f(x)=ln(x+1)+1 I tried to solve this but i got mixed up. Here is what I had. y=(x+1)+1 x=(y+1)+1 x-1=(y+1)-1 x-2=y x-2=f^-1(x) My teacher noted that I didn't add the ln to the equation upon solving. Would it be x=ln(y+1)+1 Can someone please help me. Thanks Also for the Domain, I'm guessing that I solve x+1=0 x=-1 so the domain is (-1,inf) I thought that there cannot be a domain for x<0. So confusedAnswer by jim_thompson5910(28717)   (Show Source): You can put this solution on YOUR website! So the inverse function is $\LARGE f^{-1}(x) = e^{x-1}-1$ ------------------------------------------------------- Domain of f(x): x+1 > 0 x > -1 So the domain is x > -1 which in interval notation is (-1,infinity), which is what you have. Nice job. Range of f(x): The range is the set of all real numbers since the domain of the inverse function is the set of all real numbers. Also graphing f(x) shows us that all y values get hit. Asymptote for f(x): It's the vertical asymptote x = -1 (since this value is at the boundary of the domain) ------------------------------------------------------- Let g(x) be the inverse of f(x) Domain of g(x): Set of all real numbers since you can plug in ANY number you want into and you'll get some number out. Range of g(x): The range is y > -1 which in interval notation is (-1,infinity). This is just the domain of f(x). Remember that the two switch. Asymptote for g(x): It's the horizontal asymptote y = -1 (since this value is at the boundary of the range) Again, remember that the domains, ranges, and asymptotes all switch when going from a function to its inverse.