Given function V(r) = 2gm r is the function V or r.
Where, g is the universal gravitational constant.
In order to find it's inverse we need to solve it for r first.
We have 2gm is being multiplied with r on right side.
Reverse operation of multiplication is division. So we need to divide both sides by 2gm.
[tex]\frac{V(r)}{2gm}=\frac{2gm\ r}{2gm}[/tex]
2gm crossed out on right side, we get
[tex]\frac{V(r)}{2gm}=r.[/tex]
Switching V(r) and r, we get
[tex]\frac{r}{2gm}=V(r).[/tex]
Therefore, required inverse function is
[tex]V'(r)=\frac{r}{2gm}[/tex].
