If `g(x)=(4cos^4x-2cos2x-1/2cos4x-x^7)^(1/7)` then the value of `g(g(1 – InterviewSolution

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1.	If `g(x)=(4cos^4x-2cos2x-1/2cos4x-x^7)^(1/7)` then the value of `g(g(100))` is equal toA. `-1`B. `0`C. 1D. 100
Answer» Correct Answer - D 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`

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