PLEASE HELP!!!!!!!! (ALGEBRA II)
1 answer:
Answer:
-4 4 4.5 8 20.5 32
Step-by-step explanation:
f g(x) = f(g(x))
Given, f(x) = 2x²
and g(x) = x - 2
Now f(g(x)) = f(x - 2) = 2(x - 2)²
We know that (a - b)² = a² - b² + 2ab
Using this we expand f(g(x)). We get:
f(g(x)) = 2{x² - 4x + 4}
Similarly, g(f(x)) = g(2x²) = 2x² - 2
Now, f(g(-2)) = 2[(-2)² - 4(-2) + 4] = 2(16) = 32.
Also, g(f(-2)) = 2[(-2)² - 2] = 2(2) = 4.
f(g(3.5)) = 2{(3.5)² -4(3.5) + 4} = 2[12.25 - 14 + 4] = 2(2.25) = 4.5.
g(f(3.5)) = 2{(3.5)² -2} = 2{12.25 - 2} = 2(10.25) = 20.5.
f(g(0)) = 2{0 - 4(0) + 4} = 2(4) = 8.
g(f(0)) = 2{0 - 2} = 2(-2) = -4.
Arranging them in ascending order, we get:
-4 4 4.5 8 20.5 32 would be the sequence.
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Answer: (2,1)
Step-by-step explanation:
The two equations given are:
y = 3 -x
y = x - 1
The question is asking to determine the point of intersection for two linear functions aka two lines.
Step #1: Both functions must be in slope intercept form which is y = mx+b. In this case, this step can be skipped because both functions are in slope form. At an intersection, x and y must have the same value for each equation. This means that the equations are equal to each other. Therefore, we can set both equations equal to each other to solve for x.
- Add x to both sides to get 2x - 1 = 3
- Add 1 to both sides to get 2x = 4
- Divide both sides by 2 to get x = 2
Step #2: We found the x-coordinate, but we need to find the y-coordinate. We know that the x-coordinate is 2, so substitute the number 2 into any of the given equations. So, either into y = 3 - x or y = x - 1.
The point of intersection is (2,1).
Hope this helps ^_^
