Question

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

Answer 1

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`