10) $$ \begin{array}{l} g(n)=n-1 \ h(n)=3 n-2 \ ext { Find }(g \circ h)(-4)\end{array} $$

Question

10) $$ \begin{array}{l} g(n)=n-1 \ h(n)=3 n-2 \ 	ext { Find }(g \circ h)(-4)\end{array} $$

UpStudy AI · Accepted Answer

To find $$(g \circ h)(-4)$$, we need to follow these steps:

1. **Understand the composition of functions**: The notation $$(g \circ h)(n)$$ means we first apply the function $$h$$ to $$n$$, and then apply the function $$g$$ to the result of $$h(n)$$.

2. **Calculate $$h(-4)$$**:
   - The function $$h(n)$$ is defined as $$h(n) = 3n - 2$$.
   - Substitute $$-4$$ into $$h(n)$$:
     $$
     h(-4) = 3(-4) - 2
     $$

3. **Calculate $$g(h(-4))$$**:
   - After finding $$h(-4)$$, we will use that result in the function $$g(n)$$, which is defined as $$g(n) = n - 1$$.
   - Substitute the result from $$h(-4)$$ into $$g(n)$$.

Let's perform the calculations step by step.

### Step 1: Calculate $$h(-4)$$
$$
h(-4) = 3(-4) - 2 = -12 - 2 = -14
$$

### Step 2: Calculate $$g(h(-4))$$
Now we substitute $$-14$$ into $$g(n)$$:
$$
g(-14) = -14 - 1 = -15
$$

### Final Result
Thus, $$(g \circ h)(-4) = -15$$.
$$(g \circ h)(-4) = -15$$

10) \( \begin{array}{l} g(n)=n-1 \\ h(n)=3 n-2 \\ \text { Find }(g \circ h)(-4)\end{array} \)

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