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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!=2/3` . What is the inverse of f?

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`f(x) = ( 4x + 3)/( 6x - 4), x ne (2)/(3)`
`therefore (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`
`rArr (fof) = 1 `
`rArr f = f^(-1)`
Therefore, inverse of `f` is `f^(-1) = f`
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