$$ g(n)=n^{2}+4+2 n $$ $$ h(n)=-3 n+2 $$ Find $$ (g \cdot h)(1) $$

Question

UpStudy AI · Accepted Answer

To find $$(g \cdot h)(1)$$, we first need to understand that $$(g \cdot h)(n)$$ represents the product of the functions $$g(n)$$ and $$h(n)$$. Therefore:

$$
(g \cdot h)(n) = g(n) \times h(n)
$$

Given the functions:
$$
g(n) = n^2 + 2n + 4
$$
$$
h(n) = -3n + 2
$$

Let's evaluate each function at $$n = 1$$:

1. **Calculate $$g(1)$$:**
$$
g(1) = (1)^2 + 2(1) + 4 = 1 + 2 + 4 = 7
$$

2. **Calculate $$h(1)$$:**
$$
h(1) = -3(1) + 2 = -3 + 2 = -1
$$

3. **Multiply the results:**
$$
(g \cdot h)(1) = g(1) \times h(1) = 7 \times (-1) = -7
$$

**Final Answer:** $$-7$$
$$(g \cdot h)(1) = -7$$

\( g(n)=n^{2}+4+2 n \) \( h(n)=-3 n+2 \) Find \( (g \cdot h)(1) \)

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