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JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let \(f(x) = - 1 + \left| {x - 2} \right|,\) and \(g(x) = 1 - \left| x \right|;\) then the set of all points where \(fog\) is discontinuous is
- A \(\{0,\,2\}\)
- B \(\{0,\,1,\,2\}\)
- C \(\{0\}\)
- D an empty set
Answer & Solution
Correct Answer
(D) an empty set
Step-by-step Solution
Detailed explanation
\(fog = f\left( {g\left( x \right)} \right) = f\left( {1 - \left| x \right|} \right)\) \( = - 1 + \left| {1 - \left| x \right| - 2} \right|\) \( = - 1 + \left| {\left| x \right| - 1} \right| = - 1 + \left| {\left| x \right| + 1} \right|\) let \(fog=y\)…
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