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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 off.

Let  f: R \rightarrow R be the function defined by f(x) = 1/(2 - cos x) \forall x \in R. Then, find the range off.

Answers (1)

Here, f(x) = 1/(2 - cos x) \forall x \in R

Let’s say,

\\y = 1/(2 - cos x)\\ \therefore2y - ycos x = 1\\ Or, cos x = (2y - 1)/ y\\ Or, cos x = 2 - 1/y\\

As the range of cos x is, -1 \leq cos x \leq 1\\

Therefore,

\\-1 \leq 2 - 1/y \leq 1\\ -3 \leq - 1/y \leq -1\\ 1 \leq - 1/y \leq 3\\ 1/3 \leq y \leq 1\\

Hence, the range of the given function is [1/3, 1].

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infoexpert22

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