Continuity and DifferentiabilityHard

Question

The function f(x) is

Options

A.continuous at x = 1
B.differentiable at x =1
C.diecontinuous at x =1
D.differentiable at x = 3

Solution

Here, f(x)
∴       RHL at x = 1
⇒ |1 + h - 3| = 2
        LHL at x = 1
     
     
∴     f (x) is continusous at x = 1
Again,   f(x)
∴       f′(x)
∴       differentiable at x =1
Again,   not differentiable at x =3

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