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

1 Answer
Jul 25, 2018

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]}