1.

Find all the points of discontinuity on f defined by f(x) =|x| – |x + 1|

Answer»

f(x) = |x| – |x+1| 

f(c)= |c | – |c+1| 

Let c = 0, f(0) = |0 |-|1| = 0-1= -1 

Lt f(x) = It|x| – |x + 1|= |c| – |c+1| 

x→ c X → C 

let c = 0, Lt f(x)=0 – 1 = -1 

x— +0 

∴ Lt (x→0) f(x) = f(0) = -1 

⇒ f is continuous at x =0 

There is no point of Discontinuity.


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