Question

Can someone please help me

Define the implied domain and range of y=arcsin(cosx)

This is how i did it

Let u = cosx where its range: [-1,1]

arcsin has restricted the domain [-1,1]

-1≤u≤1
-1≤cosx≤1
pi≤x≤0
0≤x≤pi

Hence, the domain of y=arcsin(cosx): [0,pi]

but how can i find the range?

Answer 1

Let f(x) = cos x
g(x) = arcsin x
\[f: Angle \rightarrow [-1,1]\]
\[g: Number \rightarrow Angle\]
and h(x) = gof (x)= g(f(x) so domain of h(x) is range of f(x). It is [-1,1]
range of h(x) is [-pi/2, pi/2]
because g just send values of f (x) only. It doesn't send anything else

Answer 2

Got what I mean?