Question

prove that f(x)=1+x+|x| is continuous​

Answer 1

Answer:

Show that f:R→R, f(x)=1/x is continuous at any c≠0.

Notice: (choose your δ so that you stay away from 0)

I hope someone can solve.

Thanks

Answer 2

Answer:

clearly f(x) is defined for every real x as

f(x) = 1+x+x = 1+2x when x>= 0

1+x-x = 1when x < 0

hence function f(x) changes at x= 0

so if f(x) is continuous at x=0, it will be continuous for all real x

now f(0)from left = 1

f(0) from right = 1+2*0 = 1

so f(0) from left = f(0) from right

hence f(x) is continuous at x= 0

so f(x) is continuous for all real x