# 25. Examine the continuity of f, where f is defined by

Given function is

Given function is defined for all real number
We, know that if two function g(x) and h(x) are continuous then g(x)+h(x) , g(x)-h(x) , g(x).h(x) allare continuous
Lets take g(x) = sin x   and    h(x) = cos x
Let suppose  x = c + h
if

Hence, function  is a continuous function
Now,
h(x) = cos x
Let suppose  x = c + h
if

Hence, function  is a continuous function
We proved independently that sin x and cos x is continous function
So, we can say that
f(x) = g(x) - h(x) = sin x - cos x is also a continuous function

When x = 0

Hence, function is also continuous at x = 0

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