Answer:
1) They are not inverses
2) They are inverses
Step-by-step explanation:
We need to find the composition function between these functions to verify if these functions are inverses. If f[g(x)] and g[f(x)] are equal to x they are inverses.
<u>1)</u>
<u>Let's find f[g(x)] and simplify.</u>
![f[g(x)]=\frac{1}{2}g(x)+\frac{3}{2}](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3D%5Cfrac%7B1%7D%7B2%7Dg%28x%29%2B%5Cfrac%7B3%7D%7B2%7D)
![f[g(x)]=\frac{1}{2}(4-\frac{3}{2}x)+\frac{3}{2}](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3D%5Cfrac%7B1%7D%7B2%7D%284-%5Cfrac%7B3%7D%7B2%7Dx%29%2B%5Cfrac%7B3%7D%7B2%7D)
![f[g(x)]=\frac{7}{2}-\frac{3}{4}x](https://tex.z-dn.net/?f=f%5Bg%28x%29%5D%3D%5Cfrac%7B7%7D%7B2%7D-%5Cfrac%7B3%7D%7B4%7Dx)
As f[g(x)] is not equal to x, these functions are not inverses.
2)
<u>Let's find f[g(x)] and simplify.</u>
![f[g(n)]=\frac{-16+(4n+16)}{4}](https://tex.z-dn.net/?f=f%5Bg%28n%29%5D%3D%5Cfrac%7B-16%2B%284n%2B16%29%7D%7B4%7D)
![f[g(n)]=\frac{-16+4n+16}{4}](https://tex.z-dn.net/?f=f%5Bg%28n%29%5D%3D%5Cfrac%7B-16%2B4n%2B16%7D%7B4%7D)
![f[g(n)]=\frac{4n}{4}](https://tex.z-dn.net/?f=f%5Bg%28n%29%5D%3D%5Cfrac%7B4n%7D%7B4%7D)
![f[g(n)]=n](https://tex.z-dn.net/?f=f%5Bg%28n%29%5D%3Dn)
Now, we need to find the other composition function g[f(x)]
<u>Let's find g[f(x)] and simplify.</u>
![g[f(x)]=4(\frac{-16+n}{4})+16](https://tex.z-dn.net/?f=g%5Bf%28x%29%5D%3D4%28%5Cfrac%7B-16%2Bn%7D%7B4%7D%29%2B16)
![g[f(x)]=-16+n+16](https://tex.z-dn.net/?f=g%5Bf%28x%29%5D%3D-16%2Bn%2B16)
![g[f(x)]=n](https://tex.z-dn.net/?f=g%5Bf%28x%29%5D%3Dn)
Therefore, as f[g(n)] = g[f(n)] = n, both functions are inverses.
I hope it helps you!
Answer:
18
Step-by-step explanation:
Alright so here you have to work backwards. the volume of a cylinder is pi*r^2*h.
Your equation: 486 pi = pi*r^2*6
You know the height is 6 feet, so you can get rid of the 6 feet hanging off of your equation by dividing both sides by 6:
81 pi = pi*r^2
Now you notice that both sides have pi. You can eliminate it by dividing both sides by pi:
81 = r^2
To isolate the r, radius, you have to take the square root of both sides, since a square root is the inverse operation of squaring. You get:
9 = r
Now that you have the radius, you can find the diameter by multiplying the radius by 2, because a diameter = 2 * the radius:
18 = d
Hope this helps!
1/6 of the wood in one hour. Let me help you with future problems i use this app called socratic it helps alot trust
The answer is C
9 - 4 = 5
5 is equal to 5
13 - 4 = 9
9 is greater than 5
The symbol means greater than or equal to
