Question

If f : R – {0} → R – {0} is defined as $f\left(x\right)=\frac{2}{3x},$ then f^–1(x) = ___________.

Answer 1

Given: A function f : R – {0} → R – {0} is defined as $f\left(x\right)=\frac{2}{3x}$

$$\begin{gathered} f\left(x\right)=\frac{2}{3x} \\ \Rightarrow y=\frac{2}{3x} \\ \Rightarrow 3x=\frac{2}{y} \\ \Rightarrow x=\frac{2}{3y} \\ \mathrm{Thus},f^{-1}\left(x\right)=\frac{2}{3x} \end{gathered}$$

Hence, if f : R – {0} → R – {0} is defined as $f\left(x\right)=\frac{2}{3x},$ then f⁻¹(x) = $\underline{\frac{2}{3x}}$.