Question

What is the domain of `f(x)=arcsin(5x-4)`?

Answer 1

Domain; `x in [ 0.6, 1 ]`.

Explanation:

The range is `y in [ -pi/2, pi/2 ]`.

Here, `X = 5x- 4 in [ - 1, 1 ]`

`rArr x in [ 0.6, 1 ]` See graph.
graph{(y-arcsin(5x-4))=0[0.6 1 -1 1]}

The inverse is #x = 0.2 sin y + 0.8, the graph of the inverse is

unrestricted. See the y-unlimited inverse wavy graph, with period `2pi` and

amplitude 0.2,

graph{x - 0.2 sin y - 0.8=0[0 2 -10 10]}