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Let f(x)=(ax + b )/(cx+d). Then the fof ...

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

A

`d=-a`

B

`d=a`

C

`a=b=1`

D

`a=b=c=d=1,`

Text Solution

Verified by Experts

The correct Answer is:
A
`fof(x)=(a[(ax+b)/(cx+d)]+b)/(c[(ax+b)/(cx+d)]+d)=x`
`therefore" "(ac+dc)x^(2)+(bc+d^(2)-bc-a^(2))x-ab-bd=0`
It is true for all real x,
`therefore" "(ac+dc)x^(2)+(bc+d^(2)-bc-a^(2))x-ab-bd =0`
`"so "a=-d`
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