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Q.

If f(x)=kxx+1, x≠−1 , then the value of k for which f(f(y))=y is

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a

2

b

−2

c

1

d

−1

answer is D.

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Detailed Solution

f(fy)=y⇒f[kyy+1]=y⇒k(kyy+1)kyy+1+1=y⇒k2yky+y+1=y ⇒k2=ky+y+1⇒k2−1=ky+y⇒(k+1)(k−1)=(k+1)y⇒(k+1)[k−1−y]=0⇒k+1=0⇒k=−1

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If f(x)=kxx+1, x≠−1 , then the value of k for which f(f(y))=y is