If f : R – {0} → R – {0} is defined as f(x)

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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