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

If the function f(x) = sqrt(2x - 3) is invertible then find its inverse. Hence prove that (fof^(-1))(x) = x

#### 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
Is there an error in this question or solution?