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

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}$

⇒ $\alpha = –1$