Given that y is inversely proportional to 𝑥

Y = 1/x          ( or was that SUPPOSED to be   y is inversely proportional to x²  ??)     

If x is halved

Y = 1/(.5x)

Y = 2/x = 2 * 1/x      Y is doubled

X increases 20%

Y = 1/(1.2x)  =   5/6  * 1/x      Y becomes  5/6 of the original