Answer
False
Work Step by Step
For example, let $f(x)=y=x$
Making x the subject, $f^{-1}(y)=x=y$
$\therefore f^{-1}(x)=x$
LHS= $f^{-1}(x)=x$
RHS= $\frac{1}{x}$
Since RHS$\neq$LHS, the statement is false
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