Question

Find the range of he inverse trigonometric function f(x)=tan^-1 (x)

Answer 1

you don't "find the range" you "define the range"

Answer 2

by convention the range of arcangent is \((-\frac{\pi}{2},\frac{\pi}{2})\)

Answer 3

how would you find that answer

Answer 4

by looking in a book
really i am not being silly
tangent is periodic, so it is certainly not one to one
you can make the inverse into a function by restricting the range of the inverse, which is the same as restricting the domain of tangent
by convention the restriction is \((-\frac{\pi}{2},\frac{\pi}{2})\)
that is just the convention, which is why you don't "find" it

Answer 5

okay i understand, so how would one define the range of he inverse trigonometric function f(x)=sin^-1 (x)

Answer 6

Same way...look in a book to see what mathematicians have decided to define as the range.

Answer 7

by convention it is \([-\frac{\pi}{2}, \frac{\pi}{2}]\)
you need only look in a text, as @Mertsj said

Answer 8

thanks :)