It is given that f(x)=(4x+3)/(6x-4),x≠2/3
(fof)(x)=f(f(x))=f[(4x+3)/(6x-4)]
=4(4x+3)/(6x-4)+3/6(4x+3)/(6x-4)-4
=16x+12+18x-12/24x+18-24x+16
=34x/35
=x.
Therefore,fof(x)=x,for all x≠2/3.
⇒fof=I.
Hence, the given function f is invertible and the inverse of f is f itself.
A school is organizing a debate competition with participants as speakers and judges. $ S = \{S_1, S_2, S_3, S_4\} $ where $ S = \{S_1, S_2, S_3, S_4\} $ represents the set of speakers. The judges are represented by the set: $ J = \{J_1, J_2, J_3\} $ where $ J = \{J_1, J_2, J_3\} $ represents the set of judges. Each speaker can be assigned only one judge. Let $ R $ be a relation from set $ S $ to $ J $ defined as: $ R = \{(x, y) : \text{speaker } x \text{ is judged by judge } y, x \in S, y \in J\} $.
The correct IUPAC name of \([ \text{Pt}(\text{NH}_3)_2\text{Cl}_2 ]^{2+} \) is: