FunctionHard
Question
If f(x) = 
, then (fof) (x) = x, provided that
, then (fof) (x) = x, provided that Options
A.d + a = 0
B.d - a = 0
C.a = b = c = d = 1
D.a = b = 1
Solution
f(x) = 
fof(x) =
fof(x) =
fof(x) =
= x
on comparing coefficient of both side (a2 + bc) x + (ab + bd) = (ac + cd) x2 + (bc + d2) x
a2 + bc = bc + d2 ⇒ a = d or a = - d
and ab + bd = 0 ⇒ b = 0 or a = - d
and ac + cd = 0 ⇒ c = 0 or a = - d
which can be simultaneously true for a = - d
fof(x) =
fof(x) =
fof(x) =
= xon comparing coefficient of both side (a2 + bc) x + (ab + bd) = (ac + cd) x2 + (bc + d2) x
a2 + bc = bc + d2 ⇒ a = d or a = - d
and ab + bd = 0 ⇒ b = 0 or a = - d
and ac + cd = 0 ⇒ c = 0 or a = - d
which can be simultaneously true for a = - d
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