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If the Function `F(X) = Sqrt(2x - 3)` is Invertible Then Find Its Inverse. Hence Prove that `(Fof^(-1))(X) = X` - Mathematics

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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`

Concept: Types of Functions
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