Question

g(x) = sin^-1(3x + 9)

domain

range

Answer 1

range [-1,1]

domain is R

Answer 2

arcsin [ u (x) ] is defined for - 1 = u (x) = 1

?

arcsin (2x + 3) is defined for :

- 1 = 2x + 3 = 1

- 1 - 3 = 2x = 1 - 3

- 4 = 2x = - 2

- 2 = x = - 1

?

Domain of arcsin (2x - 3) = [ - 2 ; - 1 ]

*******

arcsin (- 1) = - p/2

arcsin (1) = p/2

?

Range = [ - p/2 ; p/2 ]

Answer 3

domain [-10/3 , -8/3]
range (-infinity to +infinity)

Answer 4

domain = [-3,-8/3]
range = [0,2pi]

Answer 5

domain:
|3x+9|<1

-1 < 3x+9 < 1

-10/3 < x < -8/3


range:

[-pi/2,pi/2]

Answer 6

g(x) = sin^-1(3x + 9)

domain

-1<3x+9<1

-1-9<3x<1-9

-10/3<x<-8/3
so domain is [-10/3,-8/3]
range

range is [-90,90]