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Question
If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`
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Solution
Let `y = sqrt(2x -2)`
`:. y^2 = 2x - 3`
`x = (y^2 + 3)/2`
`:. f^(-1) (x) = (x^2 + 3)/2 `
Now,
L.H.S = `fof^(-1)(x) = f[f^(-1)(x)]`
`=sqrt(2f^(-1)(x) - 3)`
`= sqrt(2((x^2+ 3)/2)- 3) = x`
`:. fof^(-1)(x) = x`
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