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Let f(x)=(ax+b)/(cx+d) , x!=-d/c. If d=...

Let `f(x)=(ax+b)/(cx+d)` ,` x!=-d/c`.
If d=-a,
show that f{(x)}=x is an identity.

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Knowledge Check

  • If f (x) =(ax +b)/( cx +d) and (fof) x= x, then

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

  • Let f (x) = (ax + b)/(cx+d) , then fof(x) = x , provided that :

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

  • Let f(x) = (ax +b)/(cx + d) (da-cb ne 0, c ne0) then f(x) has

    A
    a critical point
    B
    no point of inflection
    C
    a maximum
    D
    a minimum

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    Let f (x) = (ax+b)/(cx+d), where a,b,c d are non zero If f (7) =7,f (11)=11 and f(f (x))=x for all x except -d/c. The unique number which is not is the range of f is

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