range of 1/2cosx - 1

Question

from chapter relation and function

Answer 1

If y = ½cosx - 1, then the range is the set of all possible values of y.

 

Since -1 ≤ cosx ≤ 1,

 

 -½ ≤ ½cosx ≤ ½

 

Thus, -½ - 1 ≤ ½cosx - 1 ≤ ½ - 1

 

               -3/2 ≤ ½cosx - 1 ≤ -1/2 

 

So, the range is [-3/2, -1/2]