# 32. Show that the function defined by  is a continuous function.

Given function is

given function is defined for all values of x
f = g o h ,  g(x) = |x| and h(x) = cos 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) = cos x
Let suppose  x = c + h
if

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

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