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:
12*12= 144 + 81= 225. 255/15= 15. Yes, this is a right triangle. I do not understand the question itself, but I hope this will help
Step-by-step explanation:
<span>y=(4/9)x-2
This is in slope intercept form (y=mx+b), where m is the slope.
A perpendicular line will have the opposite reciprocal of the slope.
So if the slope here is 4/9, then the perpendicular line's slope will be -9/4.
Now that you have the slope (-9/4) and a point (4, 3), you can use the point-slope formula to find the equation.
y - y</span>₁ = m(x - x₁)
y - 3 = (-9/4)(x - 4)
y - 3 = (-9/4)x + 9
y = (-9/4)x + 12
So the answer will be:
C. <span>y= -(9/4)x+12</span>
