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If f(x)=(kx)/(x+1), where xne-1andf{f(x)...

If `f(x)=(kx)/(x+1)`, where `xne-1andf{f(x)}=x" for "xne-1` then find the value of k.

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The correct Answer is:
`k=-1`
`f(f(x))=f((kx)/(x+1))=((kxx(kx))/(x+1))/((kx)/(x+1)+1)=(k^(2)x)/(kx+x+1)=(k^(2)x)/(kx+x+1)=x`.
`:.k^(2)=kx+x+1+impliesk^(2)-kx-(x+1)=0impliesk=(xpmsqrt(x^(2)+4(x+1)))/(2)=(xpm(x+2))/(2)`
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