Answer:
k=-9
Step-by-step 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, for which
[tex]g(x) = h(x) + k[/tex]
This means we need to extract g(x) from f(x) to get:
[tex]g(x) = {x}^{2} + 3 - 9[/tex]
Or
[tex]g(x) = ( {x}^{2} + 3) + (- 9)[/tex]
[tex]g(x) =h(x)+ - 9[/tex]
Therefore k=-9
