Question

f(x)=6-5sin2(x-pi/3)

Answer 1

state domain and range

Answer 2

Domain: All real numbers
Range: -6<f(x)<6, this could also be all real numbers.

Answer 3

how?

Answer 4

-1<5sin2(x-pi/3)<1
5<6-5sin2(x-pi/3)<7

Answer 5

5 and 7 are in open intervals

Answer 6

the solution sheet says D:(-oo,oo) R: [1,11]

Answer 7

oops sorry

Answer 8

6-5sin2(x-pi/3).....................

-1<=sin(x-pi/3)<=1
-5<=5sin(x-pi/3)<=5 ( on multiplying by 5)
5>=-5sin(x-pi/3)>=-5 ( on multiplying with -1)
11>=6-5sin(x-pi/3)>=1 (on adding 6)