Answer:
Value of 
is 8.
Step-by-step explanation:
Given function,
![f(x)=\big[\frac{x}{2}\big]](https://tex.z-dn.net/?f=f%28x%29%3D%5Cbig%5B%5Cfrac%7Bx%7D%7B2%7D%5Cbig%5D)
we have to find :
It is known that,
![[x]](https://tex.z-dn.net/?f=%5Bx%5D)
=the greatest integer <=x
Then,
![\implies x=f^{-1}(\big[\frac{x}{2}\big])](https://tex.z-dn.net/?f=%5Cimplies%20x%3Df%5E%7B-1%7D%28%5Cbig%5B%5Cfrac%7Bx%7D%7B2%7D%5Cbig%5D%29)
Taking x=8 we get,
![f^{-1}(\big[\frac{x}{2}\big])=x](https://tex.z-dn.net/?f=f%5E%7B-1%7D%28%5Cbig%5B%5Cfrac%7Bx%7D%7B2%7D%5Cbig%5D%29%3Dx)
![\implies f^{-1}(\big[\frac{8}{2}\big])=8](https://tex.z-dn.net/?f=%5Cimplies%20f%5E%7B-1%7D%28%5Cbig%5B%5Cfrac%7B8%7D%7B2%7D%5Cbig%5D%29%3D8)
![\implies f^{-1}([4])=8](https://tex.z-dn.net/?f=%5Cimplies%20f%5E%7B-1%7D%28%5B4%5D%29%3D8)
( Since [4]=4 )
Hence the value of is 8.
1. Match to B
2. Match to A
3. Match to D
4. Prime
Hope it helps!
Answer:
1. 1/4
2. 43/10 or 4 3/10 either are correct.
3. 67/12 or 5 7/12 either are correct.
Step-by-step explanation:
I hope this helped.
I believe the answer is C. It is the only one that makes sense
