Let f   : R → R and g   : R → R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h   : R → R by h x =   max ⁡ f x ,   g x i f x   ≤ 0 min ⁡ f x ,   g x i f x > 0 Then number of points at which h x is not…

Question

Let f &#160; : R &#8594; R and g &#160; : R &#8594; R be respectively given by f x = x + 1 and g x = x 2 + 1 . Define h &#160; : R &#8594; R by h x = &#160; max &#8289; f x , &#160; g x i f x &#160; &#8804; 0 min &#8289; f x , &#160; g x i f x &#62; 0 Then number of points at which h x is not differentiable is_________

Aicharya · Accepted Answer

h x = x 2 + 1 , x ∈ - ∞ , - 1 - x + 1 , x ∈ - 1 , 0 x 2 + 1 , x ∈ 0 , 1 x + 1 , x ∈ 1 , ∞ Hence, not differentiable at x = - 1 , 0 , 1

Let f   : R → R and g   : R → R be respectively given by f x = x + 1 and g x = x 2 + 1…

Solution

Let f &#160; : R &#8594; R and g &#160; : R &#8594; R be respectively given by f x = x + 1 and g x = x 2 + 1…

Solution

Let f : R → R and g : R → R be respectively given by f x = x + 1 and g x = x 2 + 1…