Inverse Functions
\(\blacksquare\) If \(f(x)=y\), then the inverse function is \(f^{–1}(y)=x\).
\(\blacksquare\) Only one-to-one functions have inverse functions.
\(\blacksquare\) \(f\) and \(g\) are inverse functions of each other if and only if \(fg(x)=x\), \(x\) in domain of \(g\) and\(gf(x)=x\), \(x\) in domain of \(f\).
\(\blacksquare\) If \(f\) and \(g\) are inverse functions of each other, then
(a) domain of \(f\)=range of \(g\) and domain of \(g\)=range of \(f\).
(b) graph \(g\) is the reflection of graph \(f\) on the line \(y=x\).
\(\blacksquare\) Horizontal line test can be used to test the existence of inverse functions.
\(\blacksquare\) \(ff^{–1}(x)=f^{–1}f(x)=x\)
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