The largest interval lying in ( − 2 π , 2 π ) for which the function [ f ( x ) = 4 − x 2 + cos − 1 ( 2 x − 1 ) + lo g ( cos x ) ] is defined, is

Question

The largest interval lying in ( − 2 π ​ , 2 π ​ ) for which the function [ f ( x ) = 4 − x 2 + cos − 1 ( 2 x ​ − 1 ) + lo g ( cos x ) ] is defined, is

TestHub · Accepted Answer

f ( x ) is defined if − 1 ≤ 2 x ​ − 1 ≤ 1 and cos x > 0 or 0 ≤ x ≤ 4 and − 2 π ​ < x < 2 π ​ ∴ x ∈ [ 0 , 2 π ​ ) .

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