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$Range of function f (x) = \log_{2} (\frac{π + 2 \sin^{- 1} (\frac{3 - x}{7})}{π}) is$

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(−∞,1)

(1,∞)

(−∞,1]

[1,∞)

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detailed solution

Correct option is C

-π2≤sin-13-x7≤π2⇒ -π ≤ 2 sin-13-x7≤π⇒0≤π+2sin-13-x7≤2π⇒0≤π+2 sin-13-x7π≤2⇒-∞< logπ+2 sin-13-x7π 2 ≤1 since logarithem function is defined for only positive values hence range is =(-∞,1]

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Range of function f(x)=log2⁡π+2sin−1⁡3−x7π is

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$Range of function f (x) = \log_{2} (\frac{π + 2 \sin^{- 1} (\frac{3 - x}{7})}{π}) is$