Question

The function h(x)=x^2+3 and g(x)=x^2-6. If g(x)=h(x)+k, what is the values of k?

Answer 1

The value of
`k` is -9.

Explanation:

Let
`g(x) = x^(2)-6`, we proceed to manipulate the expression algebraically to derive an expression equivalent to
`g(x) = h(x) + k`, where
`h(x) = x^(2)+3`.

`g(x) = x^(2)+[(-9)+3]` Definition of subtraction.

`g(x) = (x^(2)+3)+(-9)` Commutative and associative properties.

`g(x) = h(x) +(-9)`
`h(x) = x^(2)+3`/Result

We notice that value of
`k` is -9.