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antiseptic1488 [7]
3 years ago
8

F(x)=x -1 g(x)=-4x2 + 4 Find (f o g)(x)​

Mathematics
1 answer:
ValentinkaMS [17]3 years ago
3 0

Answer:

4x^2 + 3.

Step-by-step explanation:

f o g(x) = f(4x^2 + 4)

= (4x^2 + 4) - 1

= 4x^2 + 3.

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State the restrictions on the range for y=x^4+8x^3+k
sveticcg [70]
Answer: The range is y \ge k-432

The way to get this answer isn't completely obvious. What I did first was graph the function using GeoGebra allowing k to be a parameter. With k as a sliding parameter, the graph was able to be slid up and down the screen. The basic shape of the curve is a distorted W shape. The lowest point being the local minimum. Which is where the lower endpoint of the range would be.

Using the derivative, we can get
y = x^4 + 8x^3 + k
dy/dx = 4x^3 + 24x^2
set dy/dx equal to zero and solve for x
dy/dx = 0
4x^3 + 24x^2 = 0
4x^2(x + 6) = 0
4x^2 = 0 or x+6 = 0
x = 0 or x = -6

It turns out that x = 0 is a saddle point so we can ignore this value. Only x = -6 is where the local min is at. Plug this back into the original function

y = x^4+8x^3+k
y = (-6)^4+8(-6)^3+k
y = -432+k
y = k - 432

So when the input is x = -6, the output is k - 432 for some value k
In other words, the smallest y can get is k - 432. Otherwise it will be larger than this value

So that's why the range is y \ge k - 432

Note: if this calculus approach doesn't make much sense, then you can try various k values and use a calculator to find the lowest point. Making a table of k values with the corresponding lowest point would hopefully point you in the right direction. 
3 0
2 years ago
How many time greater is 46 than 0.46?
r-ruslan [8.4K]
46 is 100 times greater than 0.46. This is because 0.46 * 100 = 46, and 46/100 = 0.46. Hope this helps! :)
5 0
3 years ago
Please answer this...​
Romashka [77]
2 in the first column and 5 in the second column
7 0
3 years ago
A point is reflected across the x-axis. The new point is located at (4.75, -2.25) Where was the original point located.
sergejj [24]

Answer:

(4.75, 2.25)

Step-by-step explanation:

Given the coordinate (x,y). If this coordinate is reflected over the x axis, the resulting coordinate will be (x, -y)

Note that the y coordinate was negated.

Let the original point needed be (x, y)

If the new point is located at (4.75, -2.25)

Since the y coordinate was negated, then;

-y = -2.25

y = 2.25

x = 4,75 (x coordinate remains the same)

Hence the original point is (4.75, 2.25)

4 0
2 years ago
What is the solution to the inequality –2.1x + 2.9 > 15.5?
Alexandra [31]
The answer is b ......
5 0
2 years ago
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