Question

discuss the continuity of the function f(x)={|x|..plss answer me...by photo

Answer 1

here function is
y = |x |
first of all we should break modulus .

for x ≥ 0
y = x
and for x < 0
y = - x

hence,
y = { x if x ≥ 0
= { - x if x < 0

we know, any function f(x) is continuous at any point at x = a when ,
limt f(x) { x→a-} = limit f(x) {x →a+} = f(a)

now use this concept here ,

we check at x = 0 becoz x = 0 is suspicious point .

Lim |x | {x→0- } = 0
lim|x | {x →0+ } = 0
y( 0) = 0

so,
y = |x | is continuous at all real point of x