Question

How do I find the domain and range of these functions?
f(x)= sinx - 1
g(x)= cosx - 1

Answer 1

u knw the domain and range of their parent functions : sinx, cosx ?

Answer 2

-1 <= sinx <= 1 and -1 <= cosx <= 1?

Answer 3

yes, those are the ranges

Answer 4

range of sinx :-

-1 <= sinx <= 1

subtract 1 through out

-1-1 <= sinx-1 <= 1-1
-2 <= sinx-1 <= 0

so, range of sinx-1 is : [-2, 0]

Answer 5

why did you substract one?

Answer 6

cuz we're after finding range of sinx-1

Answer 7

and we knw the range of sinx

Answer 8

so subtracting 1 gives u range of sinx-1

Answer 9

What abotu cosx?

Answer 10

do it same way

Answer 11

But on my book it says that the range of sinx-1 is : [-2, 0] and that the range of cosx-1 is R... Why is that?

Answer 12

range of sinx-1 and cosx-1 is : [-2, 0]
domain of sinx-1 and cosx-1 is : R

Answer 13

Ok not I get it

Answer 14

Can I ask you one more thing?

Answer 15

yes

Answer 16

Knowing the domain and the range of these functions, how to do I find a function composition that is f(g(x))?

Answer 17

easy, f( g(x) )

domain = range of g(x)

Answer 18

so, domain of f(g(x)) = [-2, 0]

Answer 19

and the function? how can I find it?

Answer 20

oh you want to find function ?

Answer 21

yea, I'm sorry if my english is not good

Answer 22

f(x)= sinx - 1
g(x)= cosx - 1

f(g(x)) = f(cosx-1)
= sin(cosx-1) - 1

Answer 23

thats teh function

Answer 24

Ok thank you!

Answer 25

u wlc (:

Answer 26

HEY dear that is easy you have to know that cos and sin can not exceed -1 and 1 so check between this range for more write for me on www.facebook.com/beastargroup