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Let
f(x) = \frac{2x + 5}{x - 4} + \frac{x^2 + 1}{4x - 3}.
Find the inverse $f^{-1}(x)$.

 Apr 8, 2024
 #1
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A natural question to ask is: Does the inverse exist?

This is the graph of the y = f(x). Obviously, the graph does not pass the horizontal line test, and hence is not 1-1. 

The inverse function does not exist, unless you restrict the domain even more.

 Apr 8, 2024

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