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If f(x)=(4x+3)/(6x-4),\ x\ !=2/3, show t...

If `f(x)=(4x+3)/(6x-4),\ x\ !=2/3,` show that `fof(x)=x` for all `x!=2/3dot` What is the inverse of `f?`

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`(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 \ \ AA x ne 2/3`
`implies fof = 1`
Hence, the given function `f` is invertible and the inverse of `f` is `f` itself.
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