Given `A = {x : (pi)/(6) le x le (pi)/( 3)} and f(x) = cos x - x ( 1+ x )`. Find ` f (A)`.A. `[pi//6,pi//3]`B. `[-pi//3,pi-6]`C. `[(1)/(2)-(pi)/(3)(1+(pi)/(3)),(sqrt3)/(2)-(pi)/(6)(1+(pi)/(6))]`D. `[(1)/(2)+(pi)/(3)(1-(pi)/(3)),(sqrt3)/(2)+(pi)/(6)(1-(pi)/(6))]`

Given `A = {x : (pi)/(6) le x le (pi)/( 3)} and f(x) = cos x - x ( 1+

1.	Given `A = {x : (pi)/(6) le x le (pi)/( 3)} and f(x) = cos x - x ( 1+ x )`. Find ` f (A)`.A. `[pi//6,pi//3]`B. `[-pi//3,pi-6]`C. `[(1)/(2)-(pi)/(3)(1+(pi)/(3)),(sqrt3)/(2)-(pi)/(6)(1+(pi)/(6))]`D. `[(1)/(2)+(pi)/(3)(1-(pi)/(3)),(sqrt3)/(2)+(pi)/(6)(1-(pi)/(6))]`
Answer» Correct Answer - C Since f(x) is a continous decreasing functions on `[pi//6, pi//3]`. Therefore, f(x) attains every value between its minimum and maximum values `"f"(pi)/(3)=(1)/(2)-(pi)/(3)(1+(pi)/(3))` `and f((pi)/(6))=(sqrt3)/(2)-(pi)/(6)(1+(pi)/(6))"respectively"` `"Hence" f(A)="Range of f(x) "=[(1)/(2)-(pi)/(3)(1+(pi)/(3)),(sqrt(3))/(2)-(pi)/(6)(1+(pi)/(3))]`