Question -
Answer -
It isknown that if g and h are two continuousfunctions, then
are also continuous.
Ithas to proved first that g (x) = sin x and h (x)= cos x are continuous functions.
Let g (x)= sin x
It isevident that g (x) = sin x is definedfor every real number.
Let c bea real number. Put x = c + h
If x → c,then h → 0
Therefore, g isa continuous function.
Let h (x)= cos x
It isevident that h (x) = cos x is definedfor every real number.
Let c bea real number. Put x = c + h
If x → c,then h → 0
h (c) =cos c
Therefore, h isa continuous function.
Therefore, it can be concluded that
(a) f (x)= g (x) + h (x) = sin x +cos x is a continuous function
(b) f (x)= g (x) − h (x) = sin x −cos x is a continuous function
(c) f (x)= g (x) × h (x) = sin x ×cos x is a continuous function