Question:
If $f: R-\{0\} \rightarrow R-\{0\}$ is defined as $f(x)=\frac{2}{3 x}$, then $r^{-1}(x)=$
Solution:
Given: A function $f: R-\{0\} \rightarrow R-\{0\}$ is defined as $f(x)=\frac{2}{3 x}$
$f(x)=\frac{2}{3 x}$
$\Rightarrow y=\frac{2}{3 x}$
$\Rightarrow 3 x=\frac{2}{y}$
$\Rightarrow x=\frac{2}{3 y}$
Thus, $f^{-1}(x)=\frac{2}{3 x}$
Hence, if $f: R-\{0\} \rightarrow R-\{0\}$ is defined as $f(x)=\frac{2}{3 x}$, then $f^{-1}(x)=\frac{2}{3 x}$
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