Answer:
The value of [tex]k[/tex] is -9.
Step-by-step explanation:
Let [tex]g(x) = x^{2}-6[/tex], we proceed to manipulate the expression algebraically to derive an expression equivalent to [tex]g(x) = h(x) + k[/tex], where [tex]h(x) = x^{2}+3[/tex].
[tex]g(x) = x^{2}+[(-9)+3][/tex] Definition of subtraction.
[tex]g(x) = (x^{2}+3)+(-9)[/tex] Commutative and associative properties.
[tex]g(x) = h(x) +(-9)[/tex] [tex]h(x) = x^{2}+3[/tex]/Result
We notice that value of [tex]k[/tex] is -9.
