JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let the functions \(f: R \rightarrow R\) and \(g: R \rightarrow R\) be defined as \(f(x)=\left\{\begin{array}{ll}x+2, & x<0 \\ x^{2}, & x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{lr}x^{3}, & x<1 \\ 3 x-2, & x \geq 1\end{array}\right.\) Then, the number of points in \(R\) where \((fog)( x )\) is \(NOT\) differentiable is equal to
- A \(3\)
- B \(1\)
- C \(0\)
- D \(2\)
Answer & Solution
Correct Answer
(B) \(1\)
Step-by-step Solution
Detailed explanation
\(f(g(x))=\left\{\begin{array}{ll}g(x)+2, & g(x)<0 \\ (g(x))^{2}, & g(x) \geq 0\end{array}\right.\) \(=\left\{\begin{array}{ll}x^{3}+2, & x<0 \\ x^{6}, & x \in[0,1) \\ (3 x-2)^{2}, & x \in[1, \infty)\end{array}\right.\)…
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