# 33. Examine that sin | x| is a continuous function.

Given function is
f(x) = sin |x|
f(x) = h o g  , h(x) = sin x and g(x) = |x|
Now,

g(x) is defined for all real numbers k
case(i)  k < 0

Hence, g(x) is continuous when k < 0

case (ii) k > 0

Hence, g(x) is continuous when k > 0

case (iii) k = 0

Hence, g(x) is continuous when k = 0
Therefore, g(x) = |x| is continuous for all real values of x
Now,
h(x) = sin x
Let suppose  x = c + h
if

Hence, function  is a continuous function
g(x) is continuous , h(x) is continuous
Therefore, f(x) = h o g is also continuous

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