JEE Mains · Maths · STD 12 - 5. continuity and 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 \(\{5, 10, 15\}\)
- B \(\{10\}\)
- C \(\{5, 10, 15, 20\}\)
- D \(\{10, 15\}\)
Answer & Solution
Correct Answer
(A) \(\{5, 10, 15\}\)
Step-by-step Solution
Detailed explanation
\(f\left( x \right) = 15 - \left| {x - 10} \right|,x \in R\) \(f\left( {f\left( x \right)} \right) = 15 - \left| {f\left( x \right) - 10} \right|\) \( = 15 - \left| {15 - \left| {x - 10} \right| - 10} \right|\) \( = 15 - \left| {15 - \left| {x - 10} \right|} \right|\)…
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