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

Create a free account to view solution

View Solution Free
Topic: Continuity and Differentiability·Practice all Continuity and Differentiability questions

More Continuity and Differentiability Questions

Let [.] denotes the greatest integer function and f(x) = [tan2x], then...is equal to...Let f(x) = , x &#8800; 0 and f(0) = 1. The value of a and b so that f is a continuous function are -...The left hand derivative of f(x) = [x] sin (&#960; x) at x = k, k is an integer, is...If f(x) = | x - 3| and &#966; (x) = (fof) (x) when x &gt; 10, then &#966;&#8242;(x) is equal to-...