Answer:
(i) (f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = x³ + 4·x² + 5·x + 2
Step-by-step explanation:
The given functions are;
f(x) = x² + 3·x + 2
g(x) = x + 1
(i) (f - g)(x) = f(x) - g(x)
∴ (f - g)(x) = x² + 3·x + 2 - (x + 1) = x² + 3·x + 2 - x - 1 = x² + 2·x + 1
(f - g)(x) = x² + 2·x + 1
(ii) (f + g)(x) = f(x) + g(x)
∴ (f + g)(x) = x² + 3·x + 2 + (x + 1) = x² + 3·x + 2 + x + 1 = x² + 4·x + 3
(f + g)(x) = x² + 4·x + 3
(iii) (f·g)(x) = f(x) × g(x)
∴ (f·g)(x) = (x² + 3·x + 2) × (x + 1) = x³ + 3·x² + 2·x + x² + 3·x + 2 = x³ + 4·x² + 5·x + 2
(f·g)(x) = x³ + 4·x² + 5·x + 2
Answer:
3. 
2<em>C.</em> 
2<em>B.</em> 
2<em>A.</em> 
1. ![\displaystyle Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20Set-Builder%5C%3ANotation%3A%20%5Bx%7C7%2C%200%20%E2%89%A0%20x%5D%20%5C%5C%20Interval%5C%3ANotation%3A%20%28-%E2%88%9E%2C%200%29%20%E2%88%AA%20%280%2C%207%29%20%E2%88%AA%20%287%2C%20%E2%88%9E%29)
Step-by-step explanation:
3. <em>See</em><em> </em><em>above</em>.
2<em>C</em>. The keyword is ratio, which signifies division, so you would choose "III.".
2<em>B</em>. The keyword is percent, which signifies multiplication of a ratio by 100, so you would choose "I.".
2<em>A</em>. The keyword is total, which signifies addition, so you would choose "II.".
1. Base this off of the denominator. Knowing that the denominator CANNOT be zero, you will get this:
![\displaystyle x^2 - 7x \\ x[x - 7] = 0; 7, 0 = x \\ \\ Set-Builder\:Notation: [x|7, 0 ≠ x] \\ Interval\:Notation: (-∞, 0) ∪ (0, 7) ∪ (7, ∞)](https://tex.z-dn.net/?f=%5Cdisplaystyle%20x%5E2%20-%207x%20%5C%5C%20x%5Bx%20-%207%5D%20%3D%200%3B%207%2C%200%20%3D%20x%20%5C%5C%20%5C%5C%20Set-Builder%5C%3ANotation%3A%20%5Bx%7C7%2C%200%20%E2%89%A0%20x%5D%20%5C%5C%20Interval%5C%3ANotation%3A%20%28-%E2%88%9E%2C%200%29%20%E2%88%AA%20%280%2C%207%29%20%E2%88%AA%20%287%2C%20%E2%88%9E%29)
I am joyous to assist you anytime.
Answer:
X = all #'s
why?
6x+10+10x < 4(4x+3)
Combined liked terms
16x + 10 < 16x +12
you can see that there is X on both sides and the lowest one has a +10 and the highest has a +12 so it will always be greater by 2
It should be zero solutions since the lines never intersect.
I mean it could also be viewed as if they intersect at every point so I'm sorry if its wrong (the M is slightly above the N so it should be parallel)
Its perpendicular if it only intersected at one point- 1 solution
If it intersects at every point- infinitely many solutions
