Consider `f: R^+ rarr [4, oo]` given by `f(x)=x^2+4.` Show that `f` is invertible with the inverse `(f^(-1))` of `f` given by `f^(-1)\ (y)=sqrt(y-4)` , where `R^+` is the set of all non-negative real numbers.

Explanation

`f: R_+ -> [4, oo)` given by `f(x)=x^2+4`.

For one-one:

Let `f(x)=f(y)`

`implies x^2+4=y^2+4`

`implies x^2 =y^2`

`implies x=y`

`therefore f` is a one -one function.

For onto:

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