Discuss the continuity of the function f(x)=`{(x , 0 le x lt1/2 12),( 12,x=1/2),( 1-x , 1/2ltxle1):}` at the point `x=1//2` .

Explanation

Given,



`f(x)= x, 0 leq x`


LHL at `{x}=frac{1}{2}`,



`lim _{x -> frac{1}{2}^{-}} f(x)=lim _{h -> 0} f(frac{1}{2}-h)=lim _{h -> 0}(frac{1}{2}-h)=frac{1}{2}`



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