The function f(x)=1/2x-6 was replaced with f(x+k)=1/2x-4. what is the value of k

Given that the function f(x)=1/2x-6 was replaced with f(x+k)=1/2x-4, then the value of k we be as follows:
f(x)=1/2x-6
replacing x1=x+k
f(x+k)=1/2(x+k)-6
equating the above to 1/2x-4 we shall have:
1/2(x+k)-6=1/2x-4
simplifying we obtain:
1/2x+1/2k=1/2x-4
1/2k=-4
hence
k=-8