Question

Let f(x) = x - |x| then f(x) is,

Continuous ⩝×∈ R

discontinuous at x = 0

Always increasing

a constant

Solution

The correct option is **A**

Continuous ⩝×∈ R

Given function is,

f(x)=x−|x|

when x>0

f(x)=x−x=0

when x<0

f(x)=x−(−x)

=2x

∴ The graph for the above can be represented as below.

This shows that no breakage is happening at any point including at x = 0. That is the function is continuous at every point x ϵ R.

Also its not strictly increasing since in x> 0 the function is constant, that is nor then increasing nor decreasing. Suggest corrections

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