AP Calculus AB help???

[reemhashem]

Given: Let f(x) = cos(x) for 0≤ x≤ 2π
and Let g(x)= Ln(x) for all x > 0
Let S be the composition of g with f, that is, S(x)=g(f(x))

a) Find the domain of S
b) Find the range of S
c)find the zeroes of S
d) is S(x) even , odd or neither. Justify your answer.

here is what i did so far:
g(cos(x))= so S(x)=Ln(cos(x))

 

[tkhunny]

Very good with the notation. Now with the implications...

What are the Domain and Range of f(x) = cos(x)?

What are the Domain and Range of g(x) = Ln(x)?

List those and let's start thinking about it.

 

[reemhashem]

Very good with the notation. Now with the implications...

What are the Domain and Range of f(x) = cos(x)?

What are the Domain and Range of g(x) = Ln(x)?

List those and let's start thinking about it.

Cos x---> Domain (-inf,inf) , Range [-1,1]
Ln(x) ---> Domain: x>0 , Range All real

 

[tkhunny]

Okay, how about the "start thinking about it" part.

Since this is a composition, g(f(x)), what sort of relationship should there be between the Range of f(x) and the Domain of g(x)?