The correct answer is: Option 3: ![(hofog)(x)=\frac{x-14}{x+4}](https://tex.z-dn.net/?f=%28hofog%29%28x%29%3D%5Cfrac%7Bx-14%7D%7Bx%2B4%7D)
Step-by-step explanation:
Given
![f(x)=\frac{x-6}{x}\\g(x)=x+4\\h(x)=3x-2](https://tex.z-dn.net/?f=f%28x%29%3D%5Cfrac%7Bx-6%7D%7Bx%7D%5C%5Cg%28x%29%3Dx%2B4%5C%5Ch%28x%29%3D3x-2)
We have to find
![(hofog)(x)](https://tex.z-dn.net/?f=%28hofog%29%28x%29)
This will be equal to:
![h(f(g(x)))](https://tex.z-dn.net/?f=h%28f%28g%28x%29%29%29)
So we have to find the composition of (fog)(x) first
![(fog)(x) = f(g(x))\\=\frac{x+4-6}{x+4}\\=\frac{x-2}{x+4}](https://tex.z-dn.net/?f=%28fog%29%28x%29%20%3D%20f%28g%28x%29%29%5C%5C%3D%5Cfrac%7Bx%2B4-6%7D%7Bx%2B4%7D%5C%5C%3D%5Cfrac%7Bx-2%7D%7Bx%2B4%7D)
Now,
![(hofog)(x)=h(f(g(x)))\\=3(\frac{x-2}{x+4})-2\\=\frac{3x-6}{x+4}-2\\=\frac{3x-6-2(x+4)}{x+4}\\=\frac{3x-6-2x-8}{x+4}\\=\frac{x-14}{x+4}](https://tex.z-dn.net/?f=%28hofog%29%28x%29%3Dh%28f%28g%28x%29%29%29%5C%5C%3D3%28%5Cfrac%7Bx-2%7D%7Bx%2B4%7D%29-2%5C%5C%3D%5Cfrac%7B3x-6%7D%7Bx%2B4%7D-2%5C%5C%3D%5Cfrac%7B3x-6-2%28x%2B4%29%7D%7Bx%2B4%7D%5C%5C%3D%5Cfrac%7B3x-6-2x-8%7D%7Bx%2B4%7D%5C%5C%3D%5Cfrac%7Bx-14%7D%7Bx%2B4%7D)
The correct answer is: Option 3: ![(hofog)(x)=\frac{x-14}{x+4}](https://tex.z-dn.net/?f=%28hofog%29%28x%29%3D%5Cfrac%7Bx-14%7D%7Bx%2B4%7D)
Keywords: Composition, Functions
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Answer:
Step-by-step explanation:
He make 420 dollar off them 70 shirts
The question is a little vague but I believe the answer would be 16. 16 divided in half is 8. And that is 8 less than 16. < Not the answer for this question.
I didn't understand the question until Maria answered, she is completely right! Sorry for the misunderstanding.
Using translation concepts, the transformations are given as follows:
a) The function is horizontally compressed by a factor of 3 and shifted down one unit.
b) The function is shifted right 3 units and vertically stretched by a factor of 2.
<h3>What is a translation?</h3>
A translation is represented by a change in the function graph, according to operations such as multiplication or sum/subtraction in it's definition.
Item a:
The transformations are:
- x -> 3x, hence the function is horizontally compressed by a factor of 3.
- y -> y - 1, hence the function is shifted down one unit.
Item b:
The transformations are:
- x -> x - 3, hence the function is shifted right 3 units.
- y -> 2y, hence the function is vertically stretched by a factor of 2.
More can be learned about translation concepts at brainly.com/question/4521517
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Answer: i’m not sure if it’s just simplifying or factoring. but for simplifying it equals. 1/8 or .125
Explanation: calculator