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