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

Let y=f(x) ⇒y=1+αx⇒x=y−1α ⇒               f−1(y) =y−1α Now, f(x)=f−1(x) ⇒1+αx=x−1α ⇒     1+αx=1αx−1α ⇒     α=1α   and  1=−1α ⇒  α=−1