Question

show that the function defined by f(x) = |cos x | is a continuous function.

Answer 1

Let g(x) =cos x and h(x)=|x|

Now, g(x) is a cosine function, so it is continuous function in its domain i.e., $xϵR$

h(x) =|x| is the absolute valued function, so it is continuous function for all $xϵR$

$\therefore$ (hog)(x)=h[g(x)]=h(cosx)=|cosx|

Since, g(x) and h(x) are both continuous functions for all $xϵR$ so, composition of g(x) and h(x) is also a continuous function for all $xϵR$
Thus, f(x) =|con x| is a continuous function for all $xϵR$