Answer:
Step-by-step explanation:
β ∈ { 0° , 18° , 180° , 198° }
Answer:
Option 3 - f(x)= 4x, ![g(x) = \frac{1}{4}x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7Dx)
Step-by-step explanation:
To find : Which two functions are inverses of each other?
Solution :
Two functions are inverse if ![f(g(x))=x=g(f(x))](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Dx%3Dg%28f%28x%29%29)
Now, we find one by one
1) f(x)= x, g(x) = -x
![f(g(x))=f(-x)=-x\neq x](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%28-x%29%3D-x%5Cneq%20x)
Not true.
2) f(x)= 2x, ![g(x) = -\frac{1}{2}x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20-%5Cfrac%7B1%7D%7B2%7Dx)
![f(g(x))=f(-\frac{1}{2}x)=2\times(-\frac{1}{2}x)=-x\neq x](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%28-%5Cfrac%7B1%7D%7B2%7Dx%29%3D2%5Ctimes%28-%5Cfrac%7B1%7D%7B2%7Dx%29%3D-x%5Cneq%20x)
Not true.
3) f(x)= 4x, ![g(x) = \frac{1}{4}x](https://tex.z-dn.net/?f=g%28x%29%20%3D%20%5Cfrac%7B1%7D%7B4%7Dx)
![f(g(x))=f(\frac{1}{4}x)=4\times(\frac{1}{4}x)=x](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%28%5Cfrac%7B1%7D%7B4%7Dx%29%3D4%5Ctimes%28%5Cfrac%7B1%7D%7B4%7Dx%29%3Dx)
![g(f(x))=f(4x)=\frac{1}{4}\times 4x=x](https://tex.z-dn.net/?f=g%28f%28x%29%29%3Df%284x%29%3D%5Cfrac%7B1%7D%7B4%7D%5Ctimes%204x%3Dx)
i.e.
is true.
So, These two functions are inverse of each other.
4) f(x)= -8x, ![g(x) =8x](https://tex.z-dn.net/?f=g%28x%29%20%3D8x)
![f(g(x))=f(8x)=8\times(-8x)=-64x\neq x](https://tex.z-dn.net/?f=f%28g%28x%29%29%3Df%288x%29%3D8%5Ctimes%28-8x%29%3D-64x%5Cneq%20x)
Not true.
Therefore, Option 3 is correct.
Answer:
21,40,42
Step-by-step explanation:
That's it.Wish it's correct.:D