Q. 13 B5.0( 2 Votes )

Discuss the continuity of the following functions :

f(x) = sin x – cos x

Answer :

Idea : If f and g are two functions whose domains are same and both f and g are everywhere continuous then :


i) f + g is also everywhere continuous


ii) f – g is also everywhere continuous


iii) f*g is also everywhere continuous


f(x) = sin x – cos x


It is a purely trigonometric function


As sin x is continuous everywhere and cos x is also continuous everywhere for all real values of x


As f(x) is nothing but difference of two everywhere continuous function


f(x) is also everywhere continuous.


We can see this through its graph which shows no point of discontinuity.



Fig : plot of sin x + cos x


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