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Question: Range of f(x) = \(\frac{1}{1 - 2\cos x}\)is...

Range of f(x) = 11−2cos⁡x\frac{1}{1 - 2\cos x}is

A

[13,1]\left[ \frac { 1 } { 3 } , 1 \right]

B

[−1,13]\left[ - 1 , \frac { 1 } { 3 } \right]

C

(−∞,−1]∪[13,∞)( - \infty , - 1 ] \cup \left[ \frac { 1 } { 3 } , \infty \right)

D

[−13,1]\left[ - \frac { 1 } { 3 } , 1 \right]

Answer

(−∞,−1]∪[13,∞)( - \infty , - 1 ] \cup \left[ \frac { 1 } { 3 } , \infty \right)

Explanation

Solution

We have 1 ≥ cosx ≥ -1

⇒ 2 ≥ -2cosx ≥ -2

⇒ 3 ≥ 1 − 2cosx ≥ −1

⇒ 11−2cos⁡x\frac { 1 } { 1 - 2 \cos x } ∈ (-∞, -1]∪[13,∞)\left[ \frac { 1 } { 3 } , \infty \right)