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If f(x)=3x-2a n d(gof)^(-1)(x)=x-2, then...

If `f(x)=3x-2a n d(gof)^(-1)(x)=x-2,` then find the function `g(x)dot`

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We have `f(x)=3x-2`
` :. f^(-1)(x)=(x+2)/(3)`
Now `(gof)^(-1)(x)=x-2`
`implies f^(-1)og^(-1)(x)=x-2`
`implies f^(-1)(g^(-1)(x))=x-2`
`implies (g^(-1)(x)+2)/(3)=x-2`
`implies g^(-1)(x)=3x-8`
`implies g(x)=(x+8)/(3)`
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