Assertion : Let f : [0, ∞)→[0, ∞) and g : [0, ∞)→[0, ∞) be non-increasing and…
Mathematics · JEE Main · NTA Exams — Limit, Continuity and Differentiability
Assertion : Let f : [0, ∞)→[0, ∞) and g : [0, ∞)→[0, ∞) be non-increasing and non-decreasing functions respectively and h (x) = g ( f (x)). If f and g are differentiable for all points in their respective domains and h (0) = 0 then h (x) is constant function.
Reason : g (x) ∈ [0, ∞) ⇒ h (x) ≥ 0 and h´ (x) ≤ 0 .
Reason : g (x) ∈ [0, ∞) ⇒ h (x) ≥ 0 and h´ (x) ≤ 0 .
- If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
- If Assertion is true, Reason is true, Reason is not a correct explanation for Assertion.
- If Assertion is true, Reason is false.
- If Assertion is false, Reason is true.
Answer
(A) If Assertion is true, Reason is true, Reason is a correct explanation for Assertion.
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