9514 1404 393
Answer:
1. (f+g)(x) = 2x^2 +4x +2
2. (f -g)(x) = -2x^2 +4x -4
5. (f+g)(x) = x^2 +2x -1
6. (g -f)(x) = x^2 -2x -1
Step-by-step explanation:
None of these are compositions. They are only sums or differences.
(f±g)(x) = f(x) ± g(x)
__
1. (f+g)(x) = f(x) +g(x) = (4x -1) +(2x^2 +3)
(f+g)(x) = 2x^2 +4x +2
__
2. (f -g)(x) = f(x) -g(x) = (4x -1) -(2x^2 +3)
(f -g)(x) = -2x^2 +4x -4
__
5. (f +g)(x) = f(x) +g(x) = (2x) +(x^2 -1)
(f+g)(x) = x^2 +2x -1
__
6. (g -f)(x) = g(x) -f(x) = (x^2 -1) -(2x)
(g -f)(x) = x^2 -2x -1
Pythagorus Theorm
a sqr + b sqr = c sqr
25 sqr + 7 sqr = c sqr
625 + 49 = c sqr
625 + 49 = 674
c = sqr root of 674
c = 25.96 (rounded to 2dp)
Assuming the exponent is supposed to be "^2" your equation will read:
4x² + 8x - 5
It must set equal to y to be a valid function and the y must be set equal to zero to find x-intercepts.
4x² + 8x - 5 = 0
4x² - 2x + 10x - 5 = 0
2x(2x - 1) + 5(2x - 1) = 0
(2x + 5)(2x - 1) = 0
Set each binomial equal to zero.
2x + 5 = 0
2x = 0 - 5
2x = - 5
Divide both sides by 2
x = - 5/2
2x - 1 = 0
2x = 0 + 1
2x = 1
x = 1/2
Your x-intercepts are x = - 5/2, 1/2 or (- 5/2, 0) and (1/2, 0)
Composition function rule (f○g)(x) = f(g(x))
<em><u /></em><u>Given the separate functions</u>:
and
An equilateral polygon has congruent sides, like a rhombus.
An equiangular polygon has congruent interior angles, like a rectangle.
In other words: Equilateral doesn't necessarily have congruent INTERIOR angles while equiangular does have/need congruent interior angles.
