<h2>Evaluating Composite Functions</h2><h3>
Answer:</h3>
![w(f(m(2))) = 593](https://tex.z-dn.net/?f=w%28f%28m%282%29%29%29%20%3D%20593)
<h3>
Step-by-step explanation:</h3>
We can write how
will be defined but that's too much work and it's only useful when we are evaluating
with many inputs.
First let's solve for
first. As you read through this answer, you'll get the idea of what I'm doing.
Given:
![m(x) = -4x +1](https://tex.z-dn.net/?f=m%28x%29%20%3D%20-4x%20%2B1)
Solving for
:
![m(2) = -4(2) +1 \\ m(2) = -8 +1 \\ m(2) = -7](https://tex.z-dn.net/?f=m%282%29%20%3D%20-4%282%29%20%2B1%20%5C%5C%20m%282%29%20%3D%20-8%20%2B1%20%5C%5C%20m%282%29%20%3D%20-7)
Now we can solve for
, since
,
.
Given:
![f(x)=3x-1](https://tex.z-dn.net/?f=f%28x%29%3D3x-1)
Solving for
:
![f(-7)=3(-7)-1 \\ f(-7) = -21 -1 \\ f(-7) = -22](https://tex.z-dn.net/?f=f%28-7%29%3D3%28-7%29-1%20%5C%5C%20f%28-7%29%20%3D%20-21%20-1%20%5C%5C%20f%28-7%29%20%3D%20-22)
Now we are can solve for
. By now you should get the idea why
.
Given:
![w(x) = x^2 -5x -1](https://tex.z-dn.net/?f=w%28x%29%20%3D%20x%5E2%20-5x%20-1)
Solving for
:
![w(-22) = (-22)^2 -5(-22) -1 \\ w(-22) = 484 -5(-22) -1 \\ w(-22) = 484 +110 -1 \\ w(-22) = 593](https://tex.z-dn.net/?f=w%28-22%29%20%3D%20%28-22%29%5E2%20-5%28-22%29%20-1%20%5C%5C%20w%28-22%29%20%3D%20484%20-5%28-22%29%20-1%20%5C%5C%20w%28-22%29%20%3D%20484%20%2B110%20-1%20%5C%5C%20w%28-22%29%20%3D%20593)
Hey there!
The difference of a number, w, and 5 will be represented by (w – 5). Twice this would simply multiply this expression by 2, making it 2(w – 5). Finally, just set this expression equal to 2. Your equation is 2(w – 5) = 2.
To solve this, expand the two to the terms in parentheses. Then, solve the rest of the way as you would normally, using addition, subtraction, multiplication, or division to cancel out and move around terms. Remember, what you do on one side must be done to the other!
2(w – 5) = 2
(2*w – 2*5) = 2
(2w – 10) + 10 = (2) + 10
(2w) ÷ 2 = (12) ÷ 2
w = 6
Hope this helped you out! :-)
9514 1404 393
Answer:
irrational numbers
Step-by-step explanation:
The real numbers whose decimals do not end and do not repeat are irrational numbers.
__
If a decimal number ends or repeats, it can be represented by the <em>ratio</em> of two integers. That is the essence of a <em>ratio</em>nal number.
Cubic Yards to Cubic Inches Conversion 1 Cubic yard is equal to 46656 cubic inches. To convert cubic yards to cubic inches, multiply the cubic yard value by 46656.