If `g(x)=(4cos^4x-2cos2x-1/2cos4x-x^7)^(1/7)` then the value of `g(g(100))` is equal to

Options

A. `-1`
B. `0`
C. 1
D. 100

Answer

D

Explanation

We have `4cos^(4)x-2cos2x-(1)/(2)cos4x-x^(7)`
`=4cos^(4)x-2(2cos^(2)x-1)-(1)/(2)(2cos^(2)2x-1)-x^(7)`
`=4cos^(4)x-4cos^(2)x+2-(2cos^(2)x-1)^(2)+(1)/(2)-x^(7)`
`=((3)/(2)-x^(7))`
`rArr" "g(x)=((3)/(2)-x^(7))^((1)/(17))`
`rArr" "f(g(x))((3)/(2)-(g(x))^(7))^((1)/(7))=((3)/(2)-((3)/(2)-x^(7)))^((1)/(7))=x`
Hence `g(g(100))=100`