Let f ( x ) = sin x and g ( x ) = ln | x |. If the ranges of the composition functions…

Mathematics · JEE Advanced · NTA ExamsSets, Relations and Functions

Let f (x) = sin x and g(x) = ln |x|. If the ranges of the composition functions fog and gof are R1 and R2 respectively, then
  1. R1 = {u : –1 u < 1}, R2 = {v : –∞ < v < 0}
  2. R1 = {u : –< u < 0}, R2 = {v : –1 v ≤ 0}
  3. R1 = {u : –1 < u < 1}, R2 = {v : –∞ < v < 0}
  4. R1 = {u : –1 u ≤ 1}, R2 = {v : –∞ < v ≤ 0}

Answer

(C) R 1 = u : – 1 u R 2 = v : – ∞ v < 0

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