Question

What are the domain and range of Y= sec^-1 (6x) and Y=csc^-1(7x)

Answer 1

what is the domain of secx

Answer 2

the domain of sec^-1(x) is (-oo,-1]U[1, oo)

Answer 3

so what in what intervals can we have f inverse of that function

Answer 4

and by the way that the range not the domain

Answer 5

what do you mean

Answer 6

the domain of secx is all real numbers except pi/2

Answer 7

in this interval is secx invertible? no
it is not 1-1 function

Answer 8

im confused now lol

Answer 9

the picture is that we can only have f inverse of secx when we cut the function to pieces
let -pi/2<x<pi/2 be our interval now we can talk about the inverse of secx
so then the range is [1, oo)
since we are talking about inverse function of secx
it s domain should be [1, oo)
in other notation for any x>=1
hence sec(6x) domain is all x such that 6x>=1
therefore x>=1/6
the D is [1/6, oo)

Answer 10

my point is the question is very broad!
you have to pick x in the domain such that secx has an inverse

Answer 11

this the graph of secx as you can see we can't have an inverse in all of its domain
However what we can do is cut it into pieces of small intervals
pick one and do the inverse