MHT CET · Maths · Differentiation
Let \(f(x)=15-|x-10| ; x \in R\). Then, the set of all values of \(x\), at which the function \(g(x)=f(f(x))\) is not differentiable, is
- A \(\{10\}\)
- B \(\{10,15\}\)
- C \(\{5,10,15,20\}\)
- D \(\{5,10,15\}\)
Answer & Solution
Correct Answer
(D) \(\{5,10,15\}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)=15-|x-10| \\ & \Rightarrow f(f(x))=f(15-|x-10|) \\ & =15-|15-| x-10|-10| \\ & =15-|5-| x-10||\end{aligned}\)
graph has 3 corner points \(x=5, x=10\) and \(x=15\)
So, it is not differentiable at \(x \in\{5,10,15\}\)
graph has 3 corner points \(x=5, x=10\) and \(x=15\)
So, it is not differentiable at \(x \in\{5,10,15\}\)
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