IDNLearn.com connects you with a global community of knowledgeable individuals. Get accurate and detailed answers to your questions from our dedicated community members who are always ready to help.
Sagot :
Sure, let's go through the calculations step-by-step for each function and the provided results.
### Given Functions:
1. [tex]\( f(x) = 3x - 1 \)[/tex]
2. [tex]\( g(x) = 2x + 3 \)[/tex]
3. [tex]\( v(x) = x \times 7 \)[/tex]
4. [tex]\( p(x) = x + 10 \)[/tex]
### Perform Calculations:
1. Sum of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f+g \)[/tex]:
[tex]\[ f(x) + g(x) = (3x - 1) + (2x + 3) = 3x - 1 + 2x + 3 = 5x + 2 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 5(1) + 2 = 5 + 2 = 7 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 5(2) + 2 = 10 + 2 = 12 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 5(3) + 2 = 15 + 2 = 17 \)[/tex]
So, [tex]\( f+g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([7, 12, 17]\)[/tex].
2. Difference of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f-g \)[/tex]:
[tex]\[ f(x) - g(x) = (3x - 1) - (2x + 3) = 3x - 1 - 2x - 3 = x - 4 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 - 4 = -3 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 - 4 = -2 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 - 4 = -1 \)[/tex]
So, [tex]\( f-g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([-3, -2, -1]\)[/tex].
3. Quotient of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f/g \)[/tex]:
[tex]\[ \frac{f(x)}{g(x)} = \frac{3x - 1}{2x + 3} \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( \frac{3(1) - 1}{2(1) + 3} = \frac{2}{5} = 0.4 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( \frac{3(2) - 1}{2(2) + 3} = \frac{5}{7} \approx 0.714 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( \frac{3(3) - 1}{2(3) + 3} = \frac{8}{9} \approx 0.889 \)[/tex]
So, [tex]\( f/g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([0.4, 0.714, 0.889]\)[/tex].
4. Evaluation of [tex]\( v(x) \)[/tex]:
[tex]\[ v(x) = x \times 7 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 \times 7 = 7 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 \times 7 = 14 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 \times 7 = 21 \)[/tex]
So, [tex]\( v(x) \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([7, 14, 21]\)[/tex].
5. Evaluation of [tex]\( p(x) \)[/tex]:
[tex]\[ p(x) = x + 10 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 + 10 = 11 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 + 10 = 12 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 + 10 = 13 \)[/tex]
So, [tex]\( p(x) \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([11, 12, 13]\)[/tex].
### Summary of Results:
- [tex]\( f+g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([7, 12, 17]\)[/tex]
- [tex]\( f-g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([-3, -2, -1]\)[/tex]
- [tex]\( f/g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([0.4, 0.714, 0.889]\)[/tex]
- [tex]\( v(x) \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([7, 14, 21]\)[/tex]
- [tex]\( p(x) \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([11, 12, 13]\)[/tex]
So, the detailed calculations produce the expected results.
### Given Functions:
1. [tex]\( f(x) = 3x - 1 \)[/tex]
2. [tex]\( g(x) = 2x + 3 \)[/tex]
3. [tex]\( v(x) = x \times 7 \)[/tex]
4. [tex]\( p(x) = x + 10 \)[/tex]
### Perform Calculations:
1. Sum of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f+g \)[/tex]:
[tex]\[ f(x) + g(x) = (3x - 1) + (2x + 3) = 3x - 1 + 2x + 3 = 5x + 2 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 5(1) + 2 = 5 + 2 = 7 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 5(2) + 2 = 10 + 2 = 12 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 5(3) + 2 = 15 + 2 = 17 \)[/tex]
So, [tex]\( f+g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([7, 12, 17]\)[/tex].
2. Difference of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f-g \)[/tex]:
[tex]\[ f(x) - g(x) = (3x - 1) - (2x + 3) = 3x - 1 - 2x - 3 = x - 4 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 - 4 = -3 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 - 4 = -2 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 - 4 = -1 \)[/tex]
So, [tex]\( f-g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([-3, -2, -1]\)[/tex].
3. Quotient of [tex]\( f(x) \)[/tex] and [tex]\( g(x) \)[/tex], denoted as [tex]\( f/g \)[/tex]:
[tex]\[ \frac{f(x)}{g(x)} = \frac{3x - 1}{2x + 3} \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( \frac{3(1) - 1}{2(1) + 3} = \frac{2}{5} = 0.4 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( \frac{3(2) - 1}{2(2) + 3} = \frac{5}{7} \approx 0.714 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( \frac{3(3) - 1}{2(3) + 3} = \frac{8}{9} \approx 0.889 \)[/tex]
So, [tex]\( f/g \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([0.4, 0.714, 0.889]\)[/tex].
4. Evaluation of [tex]\( v(x) \)[/tex]:
[tex]\[ v(x) = x \times 7 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 \times 7 = 7 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 \times 7 = 14 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 \times 7 = 21 \)[/tex]
So, [tex]\( v(x) \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([7, 14, 21]\)[/tex].
5. Evaluation of [tex]\( p(x) \)[/tex]:
[tex]\[ p(x) = x + 10 \][/tex]
For the values [tex]\( x = 1, 2, 3 \)[/tex]:
- When [tex]\( x = 1 \)[/tex]: [tex]\( 1 + 10 = 11 \)[/tex]
- When [tex]\( x = 2 \)[/tex]: [tex]\( 2 + 10 = 12 \)[/tex]
- When [tex]\( x = 3 \)[/tex]: [tex]\( 3 + 10 = 13 \)[/tex]
So, [tex]\( p(x) \)[/tex] for [tex]\( x = 1, 2, 3 \)[/tex] is [tex]\([11, 12, 13]\)[/tex].
### Summary of Results:
- [tex]\( f+g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([7, 12, 17]\)[/tex]
- [tex]\( f-g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([-3, -2, -1]\)[/tex]
- [tex]\( f/g \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([0.4, 0.714, 0.889]\)[/tex]
- [tex]\( v(x) \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([7, 14, 21]\)[/tex]
- [tex]\( p(x) \)[/tex] at [tex]\( x = [1, 2, 3] \)[/tex] gives [tex]\([11, 12, 13]\)[/tex]
So, the detailed calculations produce the expected results.
Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is your reliable source for accurate answers. Thank you for visiting, and we hope to assist you again.
