Question

How many possible values for y are there where y = tan^-1(3)?

Answer 1

A) 1
B) 0
C) 2
D) infinite

Those are the answer choices. I chose A but it was wrong. :/ Can someone explain this please?

Answer 2

It was wrong? 0_o ... wut?

Answer 3

There are two locations (angles) where we can get \(\large\rm \tan y=3\)

But only one of them is defined for our inverse function, namely, the one in the first quadrant, ya?

Answer 4

So I can't understand how your choice was marked wrong, hmm.

Answer 5

I know :/ I was thinking maybe y = tan^-1(3) wasn't actually a function? I know Tan^-1(3) is a function and tan^-1(3) is a relation, but I thought since they put the y= in there it was a function. Frustrating lesson.

Answer 6

Tan^-1(3) is a function ?
tan^-1(3) is a relation ?
whut? 0_o

Hmm weird stuff

Answer 7

Lol. :/

Answer 8

I really dunno

Answer 9

I forgot what a relation is :P
hold on I gotta look it up

Answer 10

I think I understand it zep :) I think it's only a function if the first letter is capitalized... I was just confused because people online were saying different things.

Answer 11

Yes, this is a function \(\large\rm y=arctan(x)\)
It has one y which corresponds to x=3.
That's important actually.

If it had more than one y value corresponding to x=3,
then it wouldn't be a function.

If they wanted us to look at \(\large\rm arctan(x)\) as some type of relation, then I guess we have something different going on...

We don't need to pass our vertical line test any more.
Our relation need not be well-behaved.
We can have multiply y values for each x input.

So like... if arctan(3) corresponds to some angle y,
then it also corresponds to y+pi (since tangent is periodic in pi), ya?

Answer 12

Hmm that's weird :(
I've never seen the functional notation use capital letter..

Answer 13

Urggg :/ Now I'm confused. So it IS a function?

Answer 14

From a website...:
"blah blah blah... To differentiate between these two entities, the common practice is to use capital letters for the function and lowercase letters for the relation."

So ya, I guess you're right.
They intended for it to be the RELATION in this case.

Answer 15

This is stupid though +_+
I've never seen the inverse trigs dealt with as just relations.
So weirddddd

Answer 16

But in most math classes, is tanx usually a function?

Answer 17

Haha. So do they usually want you to restrict the range when dealing with inverse trig functions?

Answer 18

Ya in most math classes, tan^-1(x) is the function,
with restricted range.

never seen the relation before :P weird fancy stuff

Answer 19

hmmm okay. I don't like this gray area.

Answer 20

well anyway, thanks for the help.

Answer 21

:d