ANSWER
[tex]k = - 9[/tex]
EXPLANATION
The given functions are:
[tex]h(x) = {x}^{2} + 3[/tex]
and
[tex]g(x) = {x}^{2} - 6[/tex]
We want to find the value of k, if
g(x)=h(x)+k
We need to rewrite g(x) in terms of h(x)
[tex] {x}^{2} - 6 = {x}^{2} + 3 - 9[/tex]
Thus,
g(x)=h(x)+-9
This implies that
k=-9
