Question

the function f(x)=tan x is defined in such a way that f-1 is a function. what can be the domain of f(x)

Answer 1

restrict is severely

Answer 2

usual way is to restrict the domain to \((-\frac{\pi}{2},\frac{\pi}{2})\)

Answer 3

lyubas, do you mean\[f ^{-1}(x)?\]

Answer 4

yess

Answer 5

probably not

Answer 6

how did u gt tht answer? @satellite73

Answer 7

in order to have an inverse that is a function, you have to restrict the domain of tangent so that it is a one to one function. then it will have an inverse
you are not restricting the domain of \(\tan^{-1}(x)\) that domain is all real numbers

Answer 8

on that interval tangent is strictly increasing and so it a one to one function

Answer 9

how do u no its a one to one function tho?

Answer 10

there r no y's in this problem to look at

Answer 11

and how do u restrict the domain of a function?

Answer 12

I'd suggest that you, lyubas, draw a couple of periods of the tangent function. This alone would show you why you need to restrict the domain of the tangent function before you try to find the inverse function \[\tan ^{-1}x.\]

Answer 13

it is your function, you can restrict the domain any way you like

Answer 14

lyubas: in your shoes I would do an Internet search for "tangent function". this would almost surely turn up graphs of this tangent function and help you towards understanding what restrictions on the domain are necessary. Hint: tan pi/2 is undefined.

Answer 15

ahh ok thnks

Answer 16

can u help me wit more questions or u have to go?mathmale

Answer 17

Most commonly, the graph of the tangent function is depicted as beginning just after -pi/2 and ending just before pi/2.

Answer 18

so, are you comfortable with this problem, lyubas?

Answer 19

im good il do more research later to understand it betta thnks for caring :)

Answer 20

Great! Please post your next question in the usual way.

Answer 21

kk wil do