Let g : R → R be a differentiable function with g (0) = 0, g ′(0) = 0 and g ′(1) ≠ 0 …
Mathematics · JEE Advanced · NTA Exams — Limit, Continuity and Differentiability
Let g : R → R be a differentiable function with g(0) = 0,
g′(0) = 0 and g′(1) ≠ 0 . Let \[f(x)=\left\{\begin{array}{cc} \frac{x}{|x|} g(x), & x \neq 0 \\ 0, & x=0 \end{array}\right.\] and h(x) = e|x| for all x ∈ R. Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)). Then which of the following is (are) true?
g′(0) = 0 and g′(1) ≠ 0 . Let \[f(x)=\left\{\begin{array}{cc} \frac{x}{|x|} g(x), & x \neq 0 \\ 0, & x=0 \end{array}\right.\] and h(x) = e|x| for all x ∈ R. Let (foh)(x) denote f(h(x)) and (hof)(x) denote h(f(x)). Then which of the following is (are) true?
- f is differentiable at x = 0
- h is differentiable at x = 0
- foh is differentiable at x = 0
- hof is differentiable at x = 0
Answer
(D) hof is differentiable at x = 0
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