# JEE-Advanced 2015 (16/40)

**Calculus**Level 4

Let \(g:\mathbb{R} \to \mathbb{R}\) be a differentiable function with \(g(0)=0, g'(0)=0\) and \(g'(1) \neq 0\). Let \(f(x)=\begin{cases} \frac{x}{|x|} g(x) \ \ , \quad x \neq 0 \\ 0 \ \ \ , \ \quad x=0 \end{cases}\) and \(h(x)=e^{|x|}\) for all \(x \in \mathbb{R}\). Let \((foh)(x)\) denotes \(f(h(x))\) and \((hof)(x)\) denotes \(h(f(x))\). Then which of the following is (are) true ?

\[\begin{array}{} (1) \, f \ \text{is differentiable at} \ x=0 \quad \quad \quad \quad & (2) \, h \ \text{is differentiable at} \ x=0 \\ (3) \, foh \ \text{is differentiable at} \ x=0 & (4) \, hof \ \text{is differentiable at} \ x=0 \end{array}\]

**Note :**

Submit your answer as the increasing order of the serial numbers of all the correct options.

For eg, if your answer is \((1),(2)\), then submit 12 as the correct answer, if your answer is \((2),(3),(4)\), then submit 234 as the correct answer.