QuestionFind $(g \cdot h)(1)$ for $g(n)=n^{2}+4+2n$ and $h(n)=-3n+2$ .

Studdy Solution

STEP 1

Assumptions1. The function $g(n) = n^{} +4 +n$ . The function $h(n) = -3n +$
3. We need to find the value of the product of these two functions at $n =1$ , denoted as $(g \cdot h)(1)$

STEP 2

First, we need to find the product of the two functions, $g(n)$ and $h(n)$ . This can be done by multiplying the two functions together.
$(g \cdot h)(n) = g(n) \cdot h(n)$

STEP 3

Now, substitute the actual functions into the equation.
$(g \cdot h)(n) = (n^{2} + +2n) \cdot (-3n +2)$

STEP 4

Next, we need to find the value of this product at $n =1$ . We do this by substituting $n =1$ into the equation.
$(g \cdot h)(1) = (1^{2} +4 +2 \cdot1) \cdot (-3 \cdot1 +2)$

STEP 5

Now, simplify the equation.
$(g \cdot h)(1) = (1 +4 +2) \cdot (-3 +2)$

STEP 6

Continue simplifying the equation.
$(g \cdot h)(1) = \cdot -1$

STEP 7

Finally, calculate the value of $(g \cdot h)(1)$ .
$(g \cdot h)(1) =7 \cdot -1 = -7$ So, $(g \cdot h)(1) = -7$ .

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QuestionFind $(g \cdot h)(1)$ for $g(n)=n^{2}+4+2n$ and $h(n)=-3n+2$ .

Studdy Solution

STEP 1

Assumptions1. The function $g(n) = n^{} +4 +n$ . The function $h(n) = -3n +$
3. We need to find the value of the product of these two functions at $n =1$ , denoted as $(g \cdot h)(1)$

STEP 2

First, we need to find the product of the two functions, $g(n)$ and $h(n)$ . This can be done by multiplying the two functions together.
$(g \cdot h)(n) = g(n) \cdot h(n)$

STEP 3

Now, substitute the actual functions into the equation.
$(g \cdot h)(n) = (n^{2} + +2n) \cdot (-3n +2)$

STEP 4

Next, we need to find the value of this product at $n =1$ . We do this by substituting $n =1$ into the equation.
$(g \cdot h)(1) = (1^{2} +4 +2 \cdot1) \cdot (-3 \cdot1 +2)$

STEP 5

Now, simplify the equation.
$(g \cdot h)(1) = (1 +4 +2) \cdot (-3 +2)$

STEP 6

Continue simplifying the equation.
$(g \cdot h)(1) = \cdot -1$

STEP 7

Finally, calculate the value of $(g \cdot h)(1)$ .
$(g \cdot h)(1) =7 \cdot -1 = -7$ So, $(g \cdot h)(1) = -7$ .

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QuestionFind (g⋅h)(1)(g \cdot h)(1)(g⋅h)(1) for g(n)=n2+4+2ng(n)=n^{2}+4+2ng(n)=n2+4+2n and h(n)=−3n+2h(n)=-3n+2h(n)=−3n+2.

Studdy Solution

STEP 1

Assumptions1. The function g(n)=n+4+ng(n) = n^{} +4 +ng(n)=n+4+n . The function h(n)=−3n+h(n) = -3n +h(n)=−3n+3. We need to find the value of the product of these two functions at n=1n =1n=1, denoted as (g⋅h)(1)(g \cdot h)(1)(g⋅h)(1)

STEP 2

First, we need to find the product of the two functions, g(n)g(n)g(n) and h(n)h(n)h(n). This can be done by multiplying the two functions together.(g⋅h)(n)=g(n)⋅h(n)(g \cdot h)(n) = g(n) \cdot h(n)(g⋅h)(n)=g(n)⋅h(n)

STEP 3

Now, substitute the actual functions into the equation.(g⋅h)(n)=(n2++2n)⋅(−3n+2)(g \cdot h)(n) = (n^{2} + +2n) \cdot (-3n +2)(g⋅h)(n)=(n2++2n)⋅(−3n+2)

STEP 4

Next, we need to find the value of this product at n=1n =1n=1. We do this by substituting n=1n =1n=1 into the equation.(g⋅h)(1)=(12+4+2⋅1)⋅(−3⋅1+2)(g \cdot h)(1) = (1^{2} +4 +2 \cdot1) \cdot (-3 \cdot1 +2)(g⋅h)(1)=(12+4+2⋅1)⋅(−3⋅1+2)

STEP 5

Now, simplify the equation.(g⋅h)(1)=(1+4+2)⋅(−3+2)(g \cdot h)(1) = (1 +4 +2) \cdot (-3 +2)(g⋅h)(1)=(1+4+2)⋅(−3+2)

STEP 6

Continue simplifying the equation.(g⋅h)(1)=⋅−1(g \cdot h)(1) = \cdot -1(g⋅h)(1)=⋅−1

STEP 7

Finally, calculate the value of (g⋅h)(1)(g \cdot h)(1)(g⋅h)(1).(g⋅h)(1)=7⋅−1=−7(g \cdot h)(1) =7 \cdot -1 = -7(g⋅h)(1)=7⋅−1=−7So, (g⋅h)(1)=−7(g \cdot h)(1) = -7(g⋅h)(1)=−7.

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QuestionFind $(g \cdot h)(1)$ for $g(n)=n^{2}+4+2n$ and $h(n)=-3n+2$ .

Assumptions1. The function $g(n) = n^{} +4 +n$ . The function $h(n) = -3n +$
3. We need to find the value of the product of these two functions at $n =1$ , denoted as $(g \cdot h)(1)$

First, we need to find the product of the two functions, $g(n)$ and $h(n)$ . This can be done by multiplying the two functions together.
$(g \cdot h)(n) = g(n) \cdot h(n)$

Now, substitute the actual functions into the equation.
$(g \cdot h)(n) = (n^{2} + +2n) \cdot (-3n +2)$

Next, we need to find the value of this product at $n =1$ . We do this by substituting $n =1$ into the equation.
$(g \cdot h)(1) = (1^{2} +4 +2 \cdot1) \cdot (-3 \cdot1 +2)$

Now, simplify the equation.
$(g \cdot h)(1) = (1 +4 +2) \cdot (-3 +2)$

Continue simplifying the equation.
$(g \cdot h)(1) = \cdot -1$

Finally, calculate the value of $(g \cdot h)(1)$ .
$(g \cdot h)(1) =7 \cdot -1 = -7$ So, $(g \cdot h)(1) = -7$ .