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

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