Q. 155.0( 1 Vote )

If , where x ≠ –1 and f{f(x)} = x for x ≠ –1 then find the value of k.

Answer :

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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