MATH SOLVE

2 months ago

Q:
# Determine the values of x, if any, at which the function is discontinuous. At each number where f is discontinuous, state the condition(s) for continuity that are violated. (Select all that apply.)f(x) = |x − 1|The function f is discontinuous at x = 1 because f is not defined at x = 1.The function f is discontinuous at x = 1 because lim x → 1 f(x) does not exist.The function f is discontinuous at x = 1 because lim x → 1 f(x) exists, but this limit is not equal to f(1).The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x.

Accepted Solution

A:

Answer:The function f is continuous everywhere because the three conditions for continuity are satisfied for all values of x.Step-by-step explanation:The definition of continuity of a function is:A function f (x) is continuous at x = a if the following three conditions are met:f(a) exists[tex]\lim_{x \to a} f(x)[/tex] exists[tex]\lim_{x \to a} f(x)[/tex] = f(a)We check each condition when x=11) f(x)=|x-1| so f(1)=|1-1|=0The value of f(x) exits when x=12) The limit as x approaches 1 of |x-1| can be checked with lateral limits:[tex]\lim_{x \to 1^{-}} |x-1|[/tex]=0[tex]\lim_{x \to 1^{+}}|x-1|[/tex]=0Both limits have the same value to the limit exist when x approaches 1.3) [tex]\lim_{x \to 1} |x-1|[/tex]=0=f(1)The limit as x approaches 1 of f(x) is equal to the value of f(x) exits when x=1