Math  /  Algebra

Questionpresented earlier in the right sid provided at the righ to operate the box for your are the h(x)=4x22x2h(x)=4 x^{2}-2 x-2 functions Functions are provided ins g(x)=x2+xg(x)=x^{2}+x
Choose Me... Let f(x)=3x22x1f(x)=3 x^{2}-2 x-1 o. 3x22x13 x^{2}-2 x-1
Operate Me...
1. (fg)(x)(f-g)(x) - x+13x+1\frac{x+1}{3 x+1}
2. (f+h)(x)(f+h)(x) 02x22x02 x^{2}-2 x 0
3. g(x)h(x)\frac{g(x)}{h(x)}
4. (bg)(x)(b-g)(x) o. 2x22x22 x^{2}-2 x-2
5. (f(1)g(2)h(0)(f(-1) \cdot g(2) \cdot h(0) o 24 - 7x24x37 x^{2}-4 x-3 o. 24

Studdy Solution

STEP 1

1. We need to perform arithmetic operations on the given functions f(x)f(x), g(x)g(x), and h(x)h(x).
2. The goal is to evaluate specific operations and match them with the provided multiple-choice answers.
3. We should simplify each expression step-by-step to find the correct result.

STEP 2

1. Calculate (fg)(x)(f - g)(x).
2. Calculate (f+h)(x)(f + h)(x).
3. Calculate g(x)h(x)\frac{g(x)}{h(x)}.
4. Calculate (hg)(x)(h - g)(x).
5. Calculate f(1)g(2)h(0)f(-1) \cdot g(2) \cdot h(0).

STEP 3

Calculate (fg)(x)(f - g)(x).
The functions are: f(x)=3x22x1 f(x) = 3x^2 - 2x - 1 g(x)=x2+x g(x) = x^2 + x
(fg)(x)=f(x)g(x)=(3x22x1)(x2+x)(f - g)(x) = f(x) - g(x) = (3x^2 - 2x - 1) - (x^2 + x)

STEP 4

Simplify the expression: (fg)(x)=3x22x1x2x=2x23x1(f - g)(x) = 3x^2 - 2x - 1 - x^2 - x = 2x^2 - 3x - 1

STEP 5

Calculate (f+h)(x)(f + h)(x).
The functions are: f(x)=3x22x1 f(x) = 3x^2 - 2x - 1 h(x)=4x22x2 h(x) = 4x^2 - 2x - 2
(f+h)(x)=f(x)+h(x)=(3x22x1)+(4x22x2)(f + h)(x) = f(x) + h(x) = (3x^2 - 2x - 1) + (4x^2 - 2x - 2)

STEP 6

Simplify the expression: (f+h)(x)=3x22x1+4x22x2=7x24x3(f + h)(x) = 3x^2 - 2x - 1 + 4x^2 - 2x - 2 = 7x^2 - 4x - 3

STEP 7

Calculate g(x)h(x)\frac{g(x)}{h(x)}.
The functions are: g(x)=x2+x g(x) = x^2 + x h(x)=4x22x2 h(x) = 4x^2 - 2x - 2
g(x)h(x)=x2+x4x22x2\frac{g(x)}{h(x)} = \frac{x^2 + x}{4x^2 - 2x - 2}

STEP 8

Calculate (hg)(x)(h - g)(x).
The functions are: h(x)=4x22x2 h(x) = 4x^2 - 2x - 2 g(x)=x2+x g(x) = x^2 + x
(hg)(x)=h(x)g(x)=(4x22x2)(x2+x)(h - g)(x) = h(x) - g(x) = (4x^2 - 2x - 2) - (x^2 + x)

STEP 9

Simplify the expression: (hg)(x)=4x22x2x2x=3x23x2(h - g)(x) = 4x^2 - 2x - 2 - x^2 - x = 3x^2 - 3x - 2

STEP 10

Calculate f(1)g(2)h(0)f(-1) \cdot g(2) \cdot h(0).
The functions are: f(x)=3x22x1 f(x) = 3x^2 - 2x - 1 g(x)=x2+x g(x) = x^2 + x h(x)=4x22x2 h(x) = 4x^2 - 2x - 2
First, evaluate each function at the specified points: f(1)=3(1)22(1)1=3+21=4f(-1) = 3(-1)^2 - 2(-1) - 1 = 3 + 2 - 1 = 4

STEP 11

Next, evaluate: g(2)=22+2=4+2=6g(2) = 2^2 + 2 = 4 + 2 = 6

STEP 12

Finally, evaluate: h(0)=4(0)22(0)2=2h(0) = 4(0)^2 - 2(0) - 2 = -2

STEP 13

Multiply the results: f(1)g(2)h(0)=46(2)=48f(-1) \cdot g(2) \cdot h(0) = 4 \cdot 6 \cdot (-2) = -48
Solution:
1. (fg)(x)=2x23x1(f - g)(x) = 2x^2 - 3x - 1
2. (f+h)(x)=7x24x3(f + h)(x) = 7x^2 - 4x - 3
3. g(x)h(x)=x2+x4x22x2\frac{g(x)}{h(x)} = \frac{x^2 + x}{4x^2 - 2x - 2}
4. (hg)(x)=3x23x2(h - g)(x) = 3x^2 - 3x - 2
5. f(1)g(2)h(0)=48f(-1) \cdot g(2) \cdot h(0) = -48

Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord