
Range of Values Question
Hi there,
Can you help me with the following problem please?
If f(x) = 2 sin(3x  pi/2) + 5, what is the range of the values of f(x)?
I began by moving 5 over to the other side.
2 sin(3x  pi/2) =  5
sin(3x  pi/2) = 5/2
Am I going in the right direction?
Thanks
Cromlix

No, I wouldn't go in that direction. I would build up the function f(x) from the simpler components using inequalities, like this:
$\displaystyle 1\le\sin(3x\pi/2)\le 1$
$\displaystyle 2\le 2\sin(3x\pi/2)\le 2.$
How could you finish?

Hi Ackbeet,
Thank you for replying: I would proceed: 1=< sin(3x  pi/2) =< 1
2=< sin(3x  pi/2) =< 2
Add +5 to each side.
3=< sin(3x  pi/2) =< 7 Cheers, Cromlix

Right idea, but your notation is off on the last line. You want
$\displaystyle 3\le\sin(3x  \pi/2)+5 \le 7.$