Mathematics - Functions Question with Solution | TestHub

$\mathrm{y}=1+\alpha \mathrm{x}\Rightarrow \mathrm{x}=\frac{\mathrm{y}-1}{\alpha }$ $\begin{array}{rlr}& {\mathrm{f}}^{-1}(\mathrm{x})=\frac{\mathrm{x}-1}{\alpha }=\mathrm{f}(\mathrm{x})=1+\alpha \mathrm{x}\Rightarrow & \frac{\mathrm{x}-1}{\alpha }=1+\alpha \mathrm{x}\Rightarrow \mathrm{x}-1=\alpha +{\alpha }^2\mathrm{x}\end{array}$

Equating the coefficient of x

$\begin{array}{rlrl}& {\alpha }^2=1\text{ and }\alpha =-1& \alpha =\pm 1& \alpha =-1\end{array}$