JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Let f, g: \(R \rightarrow R\) be functions defined by \(f ( x )=\left\{\begin{array}{ll}{[ x ]} & , \quad x < 0 \\ |1- x | & , \quad x \geq 0\end{array}\right.\) and \(g(x)=\left\{\begin{array}{ll}e^{x}-x & , x < 0 \\ (x-1)^{2}-1 & , \quad x \geq 0\end{array}\right.\) where \([ x ]\) denote the greatest integer less than or equal to \(x\). Then, the function fog is discontinuous at exactly
- A one point
- B two points
- C three points
- D four points
Answer & Solution
Correct Answer
(B) two points
Step-by-step Solution
Detailed explanation
Check continuity at \(x =0\) and also check continuity at those \(x\) where \(g(x)=0\) \(g(x)=0 \text { at } x=0,2\) \(\operatorname{fog}\left(0^{+}\right)=-1\) \(\text { fog }(0)=0\) Hence, discontinuous at \(x =0\) \(\operatorname{fog}\left(2^{+}\right)=1\)…
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