Math / Algebra

Question10. Find $(h-g)(x)$ * 6 points $\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}$ $2 x^{4}-1$ $2 x^{4}+3$ Option 1 Option 2 $-x^{3}+3 x+3$ $-x^{3}+3 x-1$

Studdy Solution

STEP 1

What is this asking? We're given two functions, $g(x)$ and $h(x)$ , and we need to find $(h-g)(x)$ , which means we subtract $g(x)$ from $h(x)$ . Watch out! Make sure to distribute the negative sign correctly when subtracting $g(x)$ from $h(x)$ !

STEP 2

1. Define the functions
2. Set up the subtraction
3. Simplify the expression

STEP 3

Alright, we're given two awesome functions here!
We've got $g(x) = 3x + 1$ and $h(x) = x^3 - 2$ .
Let's keep these in mind as we move forward!

STEP 4

Now, we want to find $(h-g)(x)$ .
This just means we're going to subtract $g(x)$ from $h(x)$ .
So, we set it up like this: $(h-g)(x) = h(x) - g(x)$

STEP 5

Let's substitute the expressions for $h(x)$ and $g(x)$ that we defined earlier: $(h-g)(x) = (x^3 - 2) - (3x + 1)$

STEP 6

Time to simplify! Distribute the negative sign to both terms inside the second parentheses: $(h-g)(x) = x^3 - 2 - 3x - 1$

STEP 7

Now, combine the constant terms: $-2$ and $-1$ : $(h-g)(x) = x^3 - 3x - 3$

STEP 8

So, our final answer is $(h-g)(x) = x^3 - 3x - 3$ .

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Question10. Find $(h-g)(x)$ * 6 points $\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}$ $2 x^{4}-1$ $2 x^{4}+3$ Option 1 Option 2 $-x^{3}+3 x+3$ $-x^{3}+3 x-1$

Studdy Solution

STEP 1

What is this asking? We're given two functions, $g(x)$ and $h(x)$ , and we need to find $(h-g)(x)$ , which means we subtract $g(x)$ from $h(x)$ . Watch out! Make sure to distribute the negative sign correctly when subtracting $g(x)$ from $h(x)$ !

STEP 2

1. Define the functions
2. Set up the subtraction
3. Simplify the expression

STEP 3

Alright, we're given two awesome functions here!
We've got $g(x) = 3x + 1$ and $h(x) = x^3 - 2$ .
Let's keep these in mind as we move forward!

STEP 4

Now, we want to find $(h-g)(x)$ .
This just means we're going to subtract $g(x)$ from $h(x)$ .
So, we set it up like this: $(h-g)(x) = h(x) - g(x)$

STEP 5

Let's substitute the expressions for $h(x)$ and $g(x)$ that we defined earlier: $(h-g)(x) = (x^3 - 2) - (3x + 1)$

STEP 6

Time to simplify! Distribute the negative sign to both terms inside the second parentheses: $(h-g)(x) = x^3 - 2 - 3x - 1$

STEP 7

Now, combine the constant terms: $-2$ and $-1$ : $(h-g)(x) = x^3 - 3x - 3$

STEP 8

So, our final answer is $(h-g)(x) = x^3 - 3x - 3$ .

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Question10. Find (h−g)(x)(h-g)(x)(h−g)(x) * 6 points g(x)=3x+1h(x)=x3−2\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}g(x)=3x+1h(x)=x3−2​ 2x4−12 x^{4}-12x4−1 2x4+32 x^{4}+32x4+3 Option 1 Option 2 −x3+3x+3-x^{3}+3 x+3−x3+3x+3 −x3+3x−1-x^{3}+3 x-1−x3+3x−1

Studdy Solution

STEP 1

What is this asking? We're given two functions, g(x)g(x)g(x) and h(x)h(x)h(x), and we need to find (h−g)(x)(h-g)(x)(h−g)(x), which means we subtract g(x)g(x)g(x) from h(x)h(x)h(x). Watch out! Make sure to distribute the negative sign correctly when subtracting g(x)g(x)g(x) from h(x)h(x)h(x)!

STEP 2

1. Define the functions2. Set up the subtraction3. Simplify the expression

STEP 3

Alright, we're given two awesome functions here!We've got g(x)=3x+1g(x) = 3x + 1g(x)=3x+1 and h(x)=x3−2h(x) = x^3 - 2h(x)=x3−2.Let's keep these in mind as we move forward!

STEP 4

Now, we want to find (h−g)(x)(h-g)(x)(h−g)(x).This just means we're going to subtract g(x)g(x)g(x) from h(x)h(x)h(x).So, we set it up like this: (h−g)(x)=h(x)−g(x)(h-g)(x) = h(x) - g(x)(h−g)(x)=h(x)−g(x)

STEP 5

Let's **substitute** the expressions for h(x)h(x)h(x) and g(x)g(x)g(x) that we defined earlier: (h−g)(x)=(x3−2)−(3x+1)(h-g)(x) = (x^3 - 2) - (3x + 1)(h−g)(x)=(x3−2)−(3x+1)

STEP 6

Time to simplify! **Distribute** the negative sign to both terms inside the second parentheses: (h−g)(x)=x3−2−3x−1(h-g)(x) = x^3 - 2 - 3x - 1(h−g)(x)=x3−2−3x−1

STEP 7

Now, **combine** the **constant terms**: −2-2−2 and −1-1−1: (h−g)(x)=x3−3x−3(h-g)(x) = x^3 - 3x - 3(h−g)(x)=x3−3x−3

STEP 8

So, our **final answer** is (h−g)(x)=x3−3x−3(h-g)(x) = x^3 - 3x - 3(h−g)(x)=x3−3x−3.

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Question10. Find $(h-g)(x)$ * 6 points $\begin{array}{l} g(x)=3 x+1 \\ h(x)=x^{3}-2 \end{array}$ $2 x^{4}-1$ $2 x^{4}+3$ Option 1 Option 2 $-x^{3}+3 x+3$ $-x^{3}+3 x-1$

What is this asking? We're given two functions, $g(x)$ and $h(x)$ , and we need to find $(h-g)(x)$ , which means we subtract $g(x)$ from $h(x)$ . Watch out! Make sure to distribute the negative sign correctly when subtracting $g(x)$ from $h(x)$ !

1. Define the functions
2. Set up the subtraction
3. Simplify the expression

Alright, we're given two awesome functions here!
We've got $g(x) = 3x + 1$ and $h(x) = x^3 - 2$ .
Let's keep these in mind as we move forward!

Now, we want to find $(h-g)(x)$ .
This just means we're going to subtract $g(x)$ from $h(x)$ .
So, we set it up like this: $(h-g)(x) = h(x) - g(x)$

Let's substitute the expressions for $h(x)$ and $g(x)$ that we defined earlier: $(h-g)(x) = (x^3 - 2) - (3x + 1)$

Time to simplify! Distribute the negative sign to both terms inside the second parentheses: $(h-g)(x) = x^3 - 2 - 3x - 1$

Now, combine the constant terms: $-2$ and $-1$ : $(h-g)(x) = x^3 - 3x - 3$

So, our final answer is $(h-g)(x) = x^3 - 3x - 3$ .