Continuity and DifferentiabilityHard

Question

If x + | y | = 2 y, then y as a function of x is

Options

A.defined for all real x
B.continuous at x = 0
C.differentiable for all x
D.such that for x < 0

Solution

    
Since, x + | y |= 2y
⇒      
⇒      
which could be plkotted as,
Clearly, y is continuous for all x but not differentiable at x = 0.
Also,    
Thus, f(x) is defined for all x, continuous at x = o, differentiable for all
x ∈ R - {0}, for x < 0

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