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I am an adult learning Calculus. I think this is a great forum,

Ok, you know the formula for the derivative of an inverse:

$f^{-1}(x)=\frac{1}{f'(f^{-1}(x))}$

Using this, how do you answer this one?

Find $(f^{-1})'(x)$ if $f(x)=\frac{2x-1}{x+1}$

First, using Chain rule, I determined that $f'(x) = \frac{3}{(x+1)^2}$

But, I was having trouble getting the inverse of f(x).

$y=\frac{2x-1}{x+1}$

Inverse is: $x=\frac{2y-1}{y+1}$

But, I can not put this in terms of y! What do I do?

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1 Answer 1

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Hint: Is seems you have swapped the $x$ and $y$. Now multiply by $y + 1$ to obtain $$xy + x = 2y-1.$$ Given that you are trying to isolate $y$, put all the terms with a $y$ in it on the left, and all other terms on the right. Then take a common factor of $y$ out of the expression on the left hand side; the terms that remain do not contain any $y$ terms. Now there is only one other step to obtain an expression for $y$.

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