The value of the parameter $α$ for which the function $f(x) = 1+αx,α≠0$, is the inverse of itself is

-2 -1 1 2

-1

Let $f(x)=y,$ then $1+\alpha x=y$ $\$\backslash Rightarrow\; x\; =\; \backslash frac\{y-1\}\{\backslash alpha\}\$$ $\$f^\{-1\}(y)\; =\; \backslash frac\{y-1\}\{\backslash alpha\}\$$ $\Rightarrow f^{-1}(x)=\frac{x-1}{\alpha}$ Now, $f (x)= f^{-1} (x) $ $ 1+\alpha x = \frac{x-1}{\alpha}$ ⇒ $\alpha = –1$