Question

Find the range of the function `1/(2 cos x - 1)`

Answer 1

Let f(x) = `1/(2 cos x - 1)`

Range of cosine function is

– 1 ≤ cos x ≤ 1

– 2 ≤ 2 cos x ≤ 2

– 1 ≤ 2 cos x – 1 ≤ 2 – 1

– 3 ≤ 2 cos x – 1 ≤ 1

`- 1/3 ≥ 1/(2 cos x - 1) ≥ 1`

Range of f(x) `[- ∞, (-1)/3] ∪ [1, oo]`