Answer:
(a)
f(x) = x ? 5 for x < 5 and x > 5, f(x) is a polynomial functions, so f(x)
is continuous everywhere except possible at x = 5.
continuity
at x = 5
=
5 ? 5 = 0
Also
f(5) = 5 ? 5 = 0
Since
is
continuous at x = 5.
Hence
f(x) = x ? 5 is a continuous functions.
(b)is defined
if x ? 5 0
is defined
if x ? 5 0
for
x < 5 and x > 5 f(x) is a rational functions.
Therefore
f(x) is continuous function in its domain (Df)
(c)
is defined
if x + 5
For
x < ?5 and x > ?5, f(x) is a rational function. Therefore f(x) is a
continuous function in its domain.
(d) f(x) = |x ? 5|
For x < 5, f(x) = ?
(x ? 5) and for x > 5,f(x)
= x ? 5 (by
definition)
Therefore for x < 5
and x > 5, being a polynomial function, f(x) is continuous.
Now continuity at x =
5
= 0
Also f(5) = |5 ?
5| = 0
Since LHL = RHL
= f(5)
is
continuous at x = 5.
Hence f(x) = |x
? 5| is a continuous function.
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