Let b be a non-zero real number. Suppose f : ℝ → ℝ is a differentiable function such that…
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let b be a non-zero real number. Suppose f : ℝ → ℝ
is a differentiable function such that f(0) =1 . If the derivative
of f satisfies the equation \(f^{\prime}(x)=\frac{f(x)}{b^{2}+x^{2}}\)for all x ∈ ℝ, then which of the following statements
is/are TRUE?
is a differentiable function such that f(0) =1 . If the derivative
of f satisfies the equation \(f^{\prime}(x)=\frac{f(x)}{b^{2}+x^{2}}\)for all x ∈ ℝ, then which of the following statements is/are TRUE?
- If b > 0, then f is an increasing function
- If b < 0, then f is a decreasing function
- f(x)f(−x)=1 for all x ∈ℝ
- f(x) − f(−x)=0 for all x ∈ℝ
Answer
(C) f ( x ) f (− x )=1 for all x ∈ ℝ
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