Let `f(x)=(ax + b )/(cx+d)`. Then the `fof (x)=x`, provided that : `(a!=0, b!= 0, c!=0,d!=0)`

Options

A. d=-a
B. d=a
C. a=b=c=d=1
D. a=b=1

Answer

D

Explanation

Given, `f(x)=(ax+b)/(cx+b)`
`and fof(x)=x`
`Rightarrow f((ax+b)/(cx+b))=x`
`Rightarrow (a((ax+b)/(cx+b))+b)/(c((ax+b)/(cx+b))+d)=x`
`Rightarrow (x(a^(2)+bc)+ab+bd)/(x(ac+cd)+bc+d^(2))=x`
`Rightarrow d=-a`