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. Let f: R → R be the function defined by f(x) = 1/(2 – cos x) ∀ x ∈ R. Then, find the range of f.
Dear StudentGiven,f(x) = 1/(2–cos x)∀x∈RLet y = 1/(2–cos x)2y–ycos x = 1cos x = (2y - 1)/ ycos x = 2–1/yNow, we know that -1 ≤ cos x ≤ 1So,-1 ≤ 2 – 1/y ≤ 11 ≤ – 1/y ≤ 31/3 ≤ y ≤ 1Thus, the range of the given function is [1/3, 1].Thanks
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