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

It is given that $f: R→ R$ given by $f (x) = 1 + αx, α ≠ 0$ is inverse of itself.

$∴fof (x) = x$ for all $x ∈ R$

$⇒ f (f(x)) = x$ for all $x ∈ R$

$⇒ f(1+ α x) = x$ for all $x ∈ R$

$⇒1 + α (1 + α x) = x$ for all $x ∈ R$

$⇒x (α^2 -1) + (a + 1) = 0$ for all $x ∈ R$

$⇒α^2-1=0$ and $α +1=0⇒ α = -1$