The range of the function, f (x )= log_ 5(3+ cos( 3 4+x)+ cos( 4+x)+ cos( 4-x)- cos( 3 4-x)) is

Question

Accepted Answer

Correct answer: D. (d) f (x )= log 5 (3+ cos( 3 4+x)+ cos( 4+x)+ cos( 4-x)- cos( 3 4-x)) f (x )= log_ 3(3+2 cos ( 4 ) cos (x )-2 sin ( 3 4 ) sin (x )) f (x )= log_ 5(3+ 2( cosx- sinx)) Since - 2 cosx- sinx 2 ⇒ log_ 5(3+ 2(- 2) f (x ) log_ 5(3+ 2 ( 2 ))) ⇒ log_ 5 (1 ) f (x ) log_ 5 (5 ) So Range of f(x) is [0,2]

$The range of the function, f (x) = log_{5} (3 + cos (\frac{3 π}{4} + x) + cos (\frac{π}{4} + x) + cos (\frac{π}{4} - x) - cos (\frac{3 π}{4} - x)) is$

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