Answer
$f^{-1}(x) = \frac{a}{x}$
Work Step by Step
$f(x) = \frac{a}{x}$
Let $f(x) = y$
$y = \frac{a}{x}$
Swap $x$ and $y$ and then solve for $y$
$x = \frac{a}{y}$
$xy = a$
$y = \frac{a}{x}$
$f^{-1}(x) = \frac{a}{x}$
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