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# Let $f(x) = \displaystyle \frac{1}{ax+b}$ where $a$ and $b$ are nonzero constants. Find all solutions to $f^{-1}(x) = 0$. Express your answe

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Let $f(x) = \displaystyle \frac{1}{ax+b}$ where $a$ and $b$ are nonzero constants. Find all solutions to $f^{-1}(x) = 0$. Express your answer in terms of $a$ and/or $b$.

Oct 29, 2017

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y  =  ax + b

y - b =  ax

[ y - b]  /  a  =  x        swap x and y and for y write f-1 (x)

So

f-1 (x)  = [ x - b ] / a  =  0         when     b  =  x

Oct 29, 2017