. Let f: R → R be the function defined by f(x) = 1/(2 – cos x) ∀ x ∈ R. Then, find the range of f.

Dear Student

Given,
f(x) = 1/(2–cos x)∀x∈R
Let y = 1/(2–cos x)
2y–ycos x = 1
cos x = (2y - 1)/ y
cos x = 2–1/y
Now, we know that -1 ≤ cos x ≤ 1So,
-1 ≤ 2 – 1/y ≤ 1

1 ≤ – 1/y ≤ 3
1/3 ≤ y ≤ 1
Thus, the range of the given function is [1/3, 1].
Thanks