Find the range of the function: f (

Laylah Mora

Laylah Mora

Answered question

2022-05-24

Find the range of the function:
f ( x ) = cos 2 x cos x

Answer & Explanation

Larry Yates

Larry Yates

Beginner2022-05-25Added 5 answers

f ( x ) = cos 2 x cos x = ( cos x 1 2 ) 2 1 4 1 4
with equality if and only if cos x = 1 2 , i.e. x = ± π 3 + 2 π k for some k Z
Also remember cos x [ 1 , 1 ] for all x R by the definition of cos x,
so cos 2 x cos x 2 with equality if and only if cos x = 1, i.e. x = π + 2 π k for some k Z
f(x) is also continuous in R , so its range is [ 1 4 , 2 ]

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