Would anyone be able to shed some light on the method for how

>>55152
9k=3+k

>>55152
The function is defined in two parts. In order to make it continuous, you just have to make the two parts meet.

They split in x=3.

So, in x=3, the two parts need to have the same value.

Which means that:
k*32=3+k

Which leads to:
k=3/8

>>55165
fixing :

k*3^2 = 3 + k
9k = 3 + k (as in >>55158)
8k = 3
k = 3/8

Thank you