Duration: 23:44

1 views

0

Let \( g: R \rightarrow R \) be a differentiable function with
\( g(0)=0, g^{\prime}(0)=0 \) and \( g^{\prime}(1) \neq 0 \)
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 \( x \in R \). Let \( (f o h)(x) \) denotes \( f\{h(x)\} \)
and (hof) \( (x) \) denotes \( h\{f(x)\} \). Then, which of the following is/are true?
(a) \( f \) is differentiable at \( x=0 \)
(b) \( h \) is differentiable at \( x=0 \)
(c) foh is differentiable at \( x=0 \)
(d) hof is differentiable at \( x=0 \)
📲PW App Link - https://bit.ly/YTAI_PWAP
🌐PW Website - https://www.pw.live