The answer is 38.1.078125
1. f(x) = 9x² + 6x - 8
f(x) = (3x - 2)(3x + 4)
When (3x - 2) = 0, then x = 2/3
When (3x + 4) = 0, then x = -4/3
Answer: The zeros are two divided by three and negative four divided by three.
2. f(x) = 9x³ - 45x² + 36x
f(x) = 9x(x² - 5x + 4)
= 9x(x - 1)(x - 4)
When 9x = 0, then x = 0
When (x-1) = 0, then x = 1
When (x-4) = 0, then x = 4
Answer: 0, 1 and 4
3. f(x) = 4(x+7)²(x-7)³
When (x+7)² = 0, then x = -7 (twice)
When (x-7)³ = 0, then x = 7 (thrice)
Answer: 7, multiplicity 2; -7 multiplicity 3
4. The zeros of f(x) are √5, -√5, -7
The factors of f(x) are (x-√5)(x+√5)(x+7)
Note that (x-√5)(x+√5) = x² - (√5)² = x² - 5
f(x) = (x²-5)(x+7)
= x³ + 7x² - 5x - 35
Answer: f(x) = x³ + 7x² - 5x - 35
5. Expand (2x + 4)³
From Pascal's Triangle, the coefficients are 1 3 3 1
Therefore
(2x + 4)³ = 1(2x)³(4)⁰ + 3(2x)²(4)¹ + 3(2x)¹(4)² + 1(2x)⁰(4)³
= 8x³ + 48x² + 96x + 64
Answer: 8x³ + 48x² + 96x + 64
Let f = {(–2, 4), (–1, 2), (0, 0), (1, –2), (2, –5)}. Let g = {(–3, 3), (–1, 1), (0, –3), (1, –4), (3, –6)}. What is g(f(2))? -5
Andreyy89
First find the value of f(2). This is the y coordinate of the point with x = 2 as the x coordinate. Look through the set f and see that (2,-5) is one of the points. This point says x = 2 and y = -5. So f(2) = -5
We will replace the f(2) with -5 to go from this
g(f(2))
to this
g(-5)
Now repeat the same steps but for g this time
Look through the set g for a point with x coordinate of -5. That point is NOT listed. Why not? Because the x values are -3, -1, 0, 1 and 3. None of which are -5.
No such point exists.
Final Answer: The composition is undefined
