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Question
If `f(x) = (4x + 3)/(6x - 4), x ≠ 2/3` show that fof(x) = x, for all `x ≠ 2/3`. What is the inverse of f?
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Solution
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)/(34)`
= x
Therefore, fof(x) = x for all `x ≠ 2/3`.
⇒ fof = 1
Hence, the given function f is invertible and the inverse of f is f itself.
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