Question

Discuss the continuity of the function f (x) at x = 1 where f(x) = -x when x < 0
f(x)= x when 0

Answer 1

Answer:

hi

Step-by-step explanation:

Given f(x)=

x

1

At x=0

f(0)=

0

1

=∞

Hence f(x) is not defined at x=0

By given f(x)=

x

1

,x



=0

So we check for continuity except at x=0

'C' be any number except 0.

f is continuous at x=C

x→C

lim

f(x)=f(C)

f(x)=

x→C

lim

x

1

=

C

1

∴ 'f' is continous at x=C [Expect 0]

f is not continous for all x∈R∼{0}