Consider the function y=sqrt(1+cos2x)/2

Question

(everything is under the square root)

a. Can x take on any real value?
b. How large can cos 2x become? How small?
c. How large can 1+cos2x/2 become? How small?
d. What are the domain and range of the original function?

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For A, I put that x can be any real value, but the entire function would still be an irrational number.

As for B and C, I'm not exactly sure what values it's asking for. Like, how large or small can the values be without becoming a nonreal number?

And I think I could figure out D if I can figure out B and C. Help?

Thanks!

Answer 1

b. How large can cos 2x become? How small?
You need to supply the range of cos(2x).

c. How large can 1+cos2x/2 become? How small?
Similarly, you need to supply the range of (1+cos(2x))/2

These two questions help you answer #D, as you corrected pointed out.