let f(x)=max{1+sinx,1-cosx,1} for all x belongs to [0,2pi] and g(x)=max{1,|x-1|} for all x belongs to R determine f(g(x)) and g(f(x)) - Maths - Relations and Functions

Question

let f(x)=max{1+sinx,1-cosx,1} for all x belongs to [0,2pi] and
g(x)=max{1,|x-1|} for all x belongs to R determine f(g(x)) and
g(f(x)) in terms of x where max() fn will return the maximum of its
elements also find the equivalent def of f(x)and g(x)

Gyan · Answer

This is your hint
<img src=
"https://s3mn%20mnimgs%20com/img/shared/content_ck_images/ck_5f32b3611522e%20png">

let f(x)=max{1+sinx,1-cosx,1} for all x belongs to [0,2pi] and g(x)=max{1,|x-1|} for all x belongs to R determine f(g(x)) and g(f(x)) in terms of x. where max() fn will return the maximum of its elements also find the equivalent def of f(x)and g(x)