Question

f(x)=|1+x-|x|| Check whether function is continuous or not

Answer 1

F(x)=|1+x-|x||
On solving the function we get :-
F(x) = 1 for x > 0
F(x) = 1 for x = 0
F(x) = | 1 + 2x | for x < 0
So the function is continuous for all x > 0 and x < 0.
Now checking at x = 0 :-
F(0) = 1
and
Lim x → 0 F(x) = 1
So the function is continuous at x = 0 also.
Thus the given function F(x)=|1+x-|x|| is continuous for all x ϵ R