Case 1: When x<0
f(x)=−x+1 and g(x)=x2+1
At the meeting point f(x)=g(x)
x2+1=−x+1⟹x(x+1)=0
x=−1⟹y=2
g(x) and f(x) meet at point (−1,2)
Similarly in Case 2: when x≥0
f(x)=g(x)⟹x+1=x2+1⟹x2−x=0⟹x=0,1
Meeting points are (0,1) and (1,2)
From the figure
If x<−1⇒max{f(x),g(x)}=g(x)
If −1<x<0⇒max{f(x),g(x)}=f(x)
If 0<x<1⇒min{f(x),g(x)}=g(x)
If x>1⇒min{f(x),g(x)}=f(x)
Therefore, Non-differential points are (0,1),(−1,2) and (1,2)
Correct answer is 3
![808245_113846_ans_f5fc7e75b2e4469fb1362079c71ed176.png](https://search-static.byjusweb.com/question-images/toppr_ext/questions/808245_113846_ans_f5fc7e75b2e4469fb1362079c71ed176.png)