Question

Find all points of discontinuity of the given function.

f(x) =

1 − x if x ≤ 1
x + 1 if 1 < x < 3
x2 − 5 if x ≥ 3

Answer 1

evaluate the limit as x approaches 1 from the left and right.
same thing with 3. if limits are different approaching from left and right,
function is discontinuous

Answer 2

\[\lim_{x \rightarrow 1-} 1-x =0\]
\[\lim_{x \rightarrow 1+} x+1 =2\]
discontinuous at x=1, repeat process for x=3

Answer 3

Its 1

Answer 4

What about?


h(x) =

3 − 3x if x < 1
1 if x = 1
x + 3 if x > 1

Answer 5

its 1

Answer 6

f(x) =

1/x if x < 0
x if 0 ≤ x ≤ 4
4x − 3 if x > 4