What is the domain and range for #y = 6sin^-1(4x)#?

1 Answer
Jul 28, 2015

domain : #-1/4<=x<=1/4#

range : #yinRR#

Explanation:

Remember simply that the domain of any function are the values of #x# and the range is the set of values of #y#

Function : #y=6sin^-1(4x)#

Now, rearrange our function as : #y/6=sin^-1(4x)#

The corresponding #sin# function is #sin(y/6)=4x# then #x=1/4sin(y/6)#

Any #sin# function oscillates between #-1# and #1#

#=>-1<=sin(y/6)<=1#

#=>-1/4<=1/4sin(y/6)<=1/4#

#=>-1/4<=x<=1/4#

Congratulations you have just found the domain(the values of #x#)!

Now we proceed to find the values of #y#.

Starting from #x=1/4sin(y/6)#

We see that any real value of #y# can satisfy the above function.

Meaning that #y in RR#