Mathematics

Mathematics

Problem

f

is a continuous function in

[a, b]

,

g

is a continuous function in

[b, c]

. A function

h(x)

is defined as

$h(x)$	condition
$f(x)$	$\text{for } x \in [a, b]$
$g(x)$	$\text{for } x \in (b, c]$

If

f(b) = g(b)

, then a.

h(x)

has a removable discontinuity at

x = b

b.

h(x)

may or may not be continuous in

[a, c]

c.

h(b^-) = g(b^+)

and

h(b^+) = f(b^-)

d.

h(b^+) = g(b^-)

and

h(b^-) = f(b^+)

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