Question #fe7ce

1 Answer
Dec 24, 2017

See below.

Explanation:

#f(x)=8sin(3x)#

We need to rearrange this function so we have x as function of y.

#y=8sin(3x)#

#y/8=sin(3x)#

#arcsin(y/8)=arcsin(3x)=3x#

#:.#

#1/3arcsin(y/8)=x#

Substituting #y=x#

#1/3arcsin(x/8)=ycolor(white)(8888):.# #f^(-1)(x)=1/3arcsin(x/8)#

Domain:

#y=sin(x)=> -1<=y <=1#

#arcsin(x/8)=> -1<= x/8 <=1#

#->-8 <=x<=8#

#[-8 , 8 ]#