If , where x ≠ –1 and f{f(x)} = x for x ≠ –1 then find the value of k.
Given. , x ≠ –1
F(f(x)) = f()
=
=
Given that f(f(x)) = x
x =
Dividing both sides by x
1 =
kx + x + 1 =
1 – kx – (x+1) = 0
k = or k =
k = or k =
k = or k =
k = x + 1 or k = -1
As value of x is variable we take k = -1.
Therefore, k= -1